my approach is to send a scout first and let him make a report card (you don't have to wait untill they play games then), this will include and approximately value that you have to bid in order to sign the player. this will also tell that the player is interested in joining your club or not, and if the club wants to sell or not because they just attracted the player, very useful to get that report card asap.
my next step is to make a bid, I check the result on the report card and make a bid that's just 1 or 2 million beneath that, add a percentage of next sale clause of 50% to it and complete the offer, it's good to add some monthly installments as well. sometimes I declare interest but not to often, only if the player says that he "doesn"t want to be held at the club" or something like it...
it's best to get the good players early in the game (first transfer window if possible) because their value and asking price will go up as they will get more teams adding up the bidding list. and overall, just try to be in front of man city because they will buy all the gems, first season with my Arsenal team and I lost moutinho to man city, marcelo as well... they already spend 190million € on transfers in the first season.