Sneijder has been told he must accept a cut on his wages if he wants to play for Inter again.
Stramaccioni said: "I'm sure that Sneijder can make me change my mind and earn his place back in the team, because you're sitting in front of the person who has been his biggest fan since 1 April, but at the same time that's how I am: if you deserve it, I'll give you everything, when I don't think you're up to playing you don't play.
"I think Wes appreciates that just as I think anyone who gets to know me should appreciate it. I'm your biggest fan when you deserve it, when I don't think you deserve it you sit out. If I were a player that's what I'd expect as the fairest way for the coach to do things. So I expect him to change my mind and when he does that we have a starting shirt ready for him."