"Flamini will arrive tonight in Milan and will sign a four-year contract," he said after Sunday's 2-1 win over Inter.
The French midfielder's contract with the Gunners expires at the end of this season - and manager Arsene Wenger has admitted he is wary Flamini will leave.
"Frankly, I don't know [if he is staying]," said Wenger.
"But if you ask me was I overall super-confident, I would say no. He has an offer on the table which is valid until tomorrow [Monday], then we will see.
"We have done what we had to do, it is now down to him to make a decision.
"My ideal solution is that he stays, so I am not happy if he goes - but we've done everything we can.
"We can't wait until July. You could lose players if they come on the market."