So far, in fact, that the talented kid who learned his trade on the streets of Marseille is now one of the most exciting footballers in Europe, drawing comparisons to the very best in the business.
"Xavi is 31 years old, Samir is 23," ex-Arsenal defender Gilles Grimandi told BBC Sport. "If you compare Samir to Xavi when Xavi was 23, Samir is by far the better player.
"This season he's been on the same level as the world's top players and, believe me, he will get a lot better in the coming years."
High praise indeed, and Grimandi's words will be put to the test on Tuesday when Arsenal meet Barcelona in the second leg of their last-16 Champions League tie.
It was Nasri who set up the winning goal in Arsenal's 2-1 first-leg victory, but outshining the likes of Xavi and Lionel Messi on their home turf is sure to prove an even tougher assignment.
Not that the France international has ever been fazed by such tasks.
"People don't realise how difficult it is to grow up as a footballer in Marseilles when you come from the city," Grimandi said of a player who joined his local club aged nine and made his debut at 17.
Everyone knew him by the time he was 12 or 13, so he had to deal with unbelievable expectation. After every game the fans would come up to him and analyse his performance. Big, big pressure.
"He was only young but he always reacted incredibly well. He said "OK, I'm Nasri, I'd better go and do my job". And he must have done it well because look where he is today."
The £12m spent to prise Nasri from Stade Velodrome in 2008 is looking increasingly like money well spent and Grimandi is not alone in tipping him for the PFA Player of the Year award.
At the time of writing, the midfielder has scored 14 goals in 35 appearances, which is two more than he managed in his first two campaigns in north London combined.
In 2008-09 and 09-10 he attempted a total of 36 shots in the Premier League and Champions League - this term he has already upped that figure to 47.
"This is the gift of Arsene Wenger," explained Grimandi, Arsenal's chief scout in France. "He convinces players they can always do better. He made Samir believe he could improve in every department
"Arsene has known him for many years, we watched him for a long time and we knew he would be a successful signing. But the most important thing for Samir was meeting Arsene.
"It was Arsene who convinced him he had everything it takes to become the best player in the world."
Whether or not Nasri goes on to reach that target remains to be seen but Wenger's assertion that a career at the top level does not properly begin until the age of 23 can only bode well.
The explanations for his improvement are many and varied. Grimandi puts it down to the influence of Wenger while the manager himself points to Nasri's shock at missing out on France's 2010 World Cup squad, his greater physical strength, increased "efficiency" and a new-found conviction in front of goal.
Opta analysis reveals a tactical switch, with Nasri now tending to occupy a more advanced position on either flank and cutting inside more regularly than before.
He is crossing the ball fall less and completing a lower percentage of dribbles, which indicates he is trying harder to make runs off the ball and get on the end of moves rather than initiating them.
This may, of course, reflect a desire from Wenger to leave playmaking duties to captain Cesc Fabregas and the increasingly important Jack Wilshere.
Nasri would prefer to operate in an advanced central midfield role - as he did at Marseille - and he usually does so when Fabregas is out of the team (although interestingly not in the recent Carling Cup final defeat by Birmingham or Saturday's 0-0 draw with Sunderland).
When Fabregas was out injured between 18 September to 19 October, Nasri scored five goals in five games. And when Fabregas missed the period between 23 November to 13 December, Nasri scored four in four.
By contrast, he has only scored five goals in 20 games with Fabregas in the side.
"Cesc is very important for Arsenal with his passing, his runs, his goals and his general influence," Boudewijn Zenden, a former team-mate of Nasri's at Marseilles, told BBC Sport.
"If they're both on the pitch it can make it harder for one or the other to shine as much. Nasri was the key player at Marseille, whereas at Arsenal he maybe only gets to be when Cesc is out."
That said, Arsenal have fared much better this season with both men in the team - winning 70% of matches when they have played together compared to 59% when either one has been absent.
The Gunners are sure to undergo another thorough examination at the Nou Camp, where they were beaten 4-1 in last year's quarter-finals to succumb 6-3 on aggregate.
Zenden spent three years with the Catalan giants between 1998-2001, so speaks from experience when suggesting his old club will create a hostile atmosphere and come at Arsenal with unrelenting ferocity.
"Because they're 2-1 down there will be a massive build-up in the press and in the stadium, with lots of singing and banners everywhere," stated the Dutchman, who now plays for Sunderland.
"That will make Barca even more dangerous than normal. I know Arsenal have some players with pace to hit them on the counter-attack, but that's not the right way to go.
"If you leave Barca to dictate the game they will attack you in wave after wave and eventually destroy you. You have to hold a high line, play your own game and try to pressurise them."
However they approach it, Wenger's team are guaranteed a busy evening defensively and Michael ***, editor of the football tactics website Zonal Marking, feels this is another area in which Nasri can have an impact.
"It's not something people have particularly noticed but Nasri has developed his defensive game quite significantly this season," observed ***.
"In the first leg against Barca he was up against a world class attacking right-back in Dani Alves and kept him quiet almost the entire game. As soon as Wenger introduced Andrey Arshavin, Nasri moved to the right and suddenly Alves was constantly getting forward.
"If you look back to last season's visit of Chelsea to the Emirates, Nasri faced Ashley Cole and Cole beat him twice before crossing for goals. That isn't happening any more."
Nasri, born in France to Algerian parents, grew up admiring fellow Marseilles natives Eric Cantona and Zinedine Zidane but his all-time hero was Diego Maradona and he "loves" the Barcelona style of football.
Indeed, he seems the type of player who would fit perfectly into Pep Guardiola's squad, with his speed, skill, mobility and intelligence.
"At Marseille you learn football the way it's still played on the streets," Zenden recalled. "They're very much into one-against-one situations where you try to make a fool out of your opponent.
"Kids like Nasri grow up playing in the streets and you can't really tackle on concrete, so it's all about technique. When you manage to nutmeg someone it's the ultimate satisfaction!
"Marseille have always had influences from north Africa; they've got this heated mentality which makes them want players to dribble past one or two opponents before passing the ball. They don't like simple football, they want something to look at and admire."
Nasri came through the French youth system alongside the likes of Karim Benzema, Hatem Ben Arfa, Loic Remy and Jeremy Menez but Grimandi feels he had one particular quality that set him apart from his peers.
"All five of them were born in 1987 and had immense talent," stated the 40-year-old. "When they played together for France at age group level it was near-impossible to say who was the best.
"What separated Samir was his intelligence. I had never spoken to him before he signed but you could just smell his intelligence - and intelligence is a very important factor when we look at signing a player.
"Samir is a student of football - he lives for the game. He loves training and watches game after game on TV. Name any player and he'll tell you about them. It's very rare to find players like Samir."
This reinforces Grimandi's belief that Nasri is starting to warrant mention in the same breath as some of Barcelona's mesmeric stars.
"All of these players - Fabregas, Nasri, Messi, Xavi, Andres Iniesta - are all very intelligent," he added. "Modern football is tight and if you don't think about what you're going to do with the ball before it arrives and if you don't have technical ability to do it, you won't survive.
"These guys are small in stature and can work in a short space, they play at the right tempo, they go to the right places and they make the right decisions.
"If you physically dominate the game, fair enough - but your limit will come. Physicality is not enough any more because nowadays every team is ready for the physical challenge."
Nasri has come a long way - on Tuesday he will attempt to show just how far.
