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, Paris St Germain and Tottenham.
Stramaccioni has always maintained that Sneijder's prolonged absence from the first team has been a tactical decision and on Friday he 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.