Doubt it. Either of Liverpool or City are interested, he will go there. Not to mention Madrid/Barcelona. And if PSG win the CL this time around, they become a bit more attractive too, despite the crowd and France.
The problem is that all those teams are at the top of their respective leagues. And almost all of them could easily use a talent like Sancho. Other than Liverpool, nobody has a player who has nailed the RW role in those teams (well, City, if Sterling is playing on the right).
While we have been playing well, and showing slight improvements (I still have my doubts about Ole, but definitely an improvement overall on Mou - still feel he is the manager to set the squad right and get the right players for the next coach), we aren't at the top yet, and we won't be for atleast 2 years (with the right transfers and an improvement in our tactics/playing style).
The only chance next season depends on whether or not people are allowed back in football stadiums next year. If it's the same as this year, well, no club will be able to afford Sancho. If people are allowed back, and clubs start making revenue, then it's anybody's ball game.