The Holland international has not featured for the Nerazzurri since September as a dispute over his contract rumbles on at the San Siro, with reports in Italy and England linking the 28-year-old with AC Milan, PSG and Tottenham.
Stramaccioni has always maintained that Sneijder's prolonged absence from the first team has been a tactical decision and suggested that the playmaker could have a future in Milan.
He told Gazzetta.it: "As far as Sneijder is concerned, he knows that when a player gives their all, I give them mine in return. Otherwise, they stay out (of contention).
"If I was a player I'd try to think about what my manager was thinking. I'm sure that Wesley can make me change my mind and, if he does, the shirt is waiting for him."
Sneijder, who won the treble under Jose Mourinho in 2010, has two and a half years remaining on his contract but is unhappy with Inter's request that he take a two million euro cut on his annual salary.
Inter defender Andrea Ranocchia, meanwhile, has been suspended for two matches for confronting the fourth official at the end of Saturday's meeting with Genoa.
The 24-year-old, who has also been fined 10,000 euros, has been punished for using a "provocative expression" towards the official following a 1-1 draw at the San Siro.
A statement on the Lega Serie A's official website confirmed that the fact Ranocchia had already been booked for improper conduct during the match was taken into consideration.
The defender should now miss Inter's trip to Udinese on January 6 and the subsequent visit of Pescara on January 16, should any appeal be unsuccessful.