The Italian giants' vice-president Adriano Galliani revealed they are considering selling the 32-year-old.
"There is an important negotiation with Monaco regarding Vieri," said Galliani. "In the next few days we will see whether the talks can be successful."
Vieri, who joined AC from fierce rivals Inter, has failed to make a serious impact with Andriy Shevchenko and Alberto Gilardino ahead of him in the pecking order.