The Ghanaian is desperate for regular playing time ahead of the World Cup this summer and could head out on loan or be sold in January.
After Wednesday's 3-0 win at Southampton, Mourinho suggested that Essien could stay if he was happy to be part of the Blues squad but said he could not guarantee him regular minutes.
"I offer nobody - not Michael, not nobody (guaranteed playing time)," the Portuguese said.
"I understand that players think about national team, the World Cup and playing regularly, but my players have to think of the team before the players. Michael knows that perfectly."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball