Owner Roman Abramovich is unhappy with senior players criticising the manager and is set to clear-out a number of first team stars in the summer.
According to The Sun, a club insider was quoted as saying:
"When the players question the manager, they are questioning the owner's judgment.
"Andre Villas-Boas was Mr Abramovich's personal choice. In the past, the senior players have sometimes got their way over an unpopular manager.
"But this time Mr Abramovich is fed up with their moaning."
Frank Lampard is another player who may find his future at the club under threat.
Cole, Lampard and Essien were dropped from the team against Napoli and after the game Cole supposedly told Villas-Boas that he wont win any trophies with his current tactics.