The midfielder has made just five starts for the Rossoneri this season, and is free to talk to other clubs.
"I don't know what will happen, but I believe he will not renew with Milan," Fabrizio Ferrari told ItalianFootballDaily.
"Essien is happy at Milan, he could remain but it is doubtful. It's a bit early to predict what will happen in June.
"Milan is a prestigious club which is difficult to get into, but also difficult for a player to want to leave it."