Essien has had wretched luck with injuries in the past couple of years and ruptured his anterior cruciate ligament in the summer. It was initially feared that he could be sidelined for the whole of the campaign, but he has made giant strides and could play again this year.
"Essien is making good progress and we're thinking end of December," Villas-Boas said.
Didier Drogba recently had surgery to remove a metal plate dating back to an injury in 2010 and is on target to face Liverpool.
"Didier will start training as we enter the second week of the international break and we hope he'll be available for the Liverpool game," Villas-Boas said.