Essien has been out of action since damaging his medial ligaments while training with the Ghana squad during January's Africa Cup of Nations tournament in Angola.
The former Olympique Lyonnais star is currently in France undergoing rehabilitation with Ashley Cole, and Blues assistant boss Ray Wilkins reported earlier this week that both players were progressing well.
However, an unnamed source is quoted as saying: "The news on Michael's not good. We all thought he'd be back playing again in four to six weeks.
"The second leg of the Champions League match with Inter Milan was talked about as the ideal comeback game.
"But he has no chance of making that now. We're not even sure he'll play again this season. If he does it won't be any time soon."
This would come as a cruel blow to Chelsea, who recently confirmed that Portuguese wing-back Jose Bosingwa would not play any further part in the current campaign.
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