
The top-rated French midfielder has yet to sign a new contract at Emirates Stadium despite the fact that negotiations opened in December.
Arsenal have yet to meet his financial demands - said to be in the region of £55,000 per week - and the player is getting frustrated.
Bayern Munich have joined Juventus and AC Milan among the clubs showing a keen interest in the 24-year-old, with all three well aware that his existing deal with Arsenal expires in the summer.
Wenger, however, insists that his landsman has his heart set on staying.“We are getting close to 'yes' or 'no',” Wenger revealed.
“He wants to stay and I believe him. But as long as he has not signed, he is free to sign where he wants. We have set ourselves a target at the end of April to finalise the situation, one way or the other.
“April is an absolute deadline because, afterwards, we have to make decisions in the transfer market."
There was also a veiled but very clear warning, though. "My first target is to keep the team together, but we want to continue to respect our wage structure. That is very important. Flamini has to fit in that,” concluded Wenger.