Essien was injured playing for Ghana against Libya on Friday.
A Blues insider told the Sun: “After undergoing an examination, Michael’s injury seems to be a lot worse than previously thought. He may have to have an operation.”
The player’s agent Fabien Piveteau said: “Unfortunately it’s not good news.
“I am afraid it’s a big problem. A big problem.
“He’s taken a bad blow to the knee. I don’t know exact details but I think it’s not good.
“I don’t know what will happen. It’s now two or three times that he has taken blows to his knee.”