Essien, who spent last season on loan at Real Madrid, has made just nine appearances for Chelsea this term and is said to be close to a move to San Siro.
The Ghana international joined Chelsea from Lyon in 2005, but his long association with the London club could soon come to an end after Mourinho confirmed that Chelsea are open to his departure.
"Michael Essien is at this moment in a position where he can go or he can stay," Mourinho said.
"If he stays we are more than happy, he is a fantastic club man, but he is another player that gave everything to this club and if something big comes to him, he is another we feel we must show him the respect.
"If he stays, he stays and if he stays he is playing against Stoke next weekend (on Sunday). A player we are more than happy if he stays."
Milan have endured a disappointing season so far and sit 11th in Serie A, but their squad has been bolstered by the signings of attacking midfielder Keisuke Honda and defender Adil Rami.
Former Netherlands international Clarence Seedorf replaced Massimiliano Allegri as Milan coach earlier this month, beginning his tenure with a 1-0 win over Verona, before suffering a 2-1 defeat to Udinese in the Coppa Italia quarter-finals.
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