The defender, 29, sustained the injury during the Blues' 2-1 loss to Everton midweek when he was involved in a challenge with Landon Donovan.
There is already an element of speculation as to whether the full back will have sufficiently recovered in order to book his ticket to South Africa with the rest of the England squad for the World Cup finals in the summer.
Ancelotti, though, is alleged to have said that there is a chance that Cole will return prior to the season's conclusion.
Wayne Bridge and Stephen Warnock are the favourites to deputise when the Three Lions take on Egypt in an international friendly on March 3.
Versatile Russian Yuri Zhirkov is expected to fulfill Cole's duties at Chelsea.