The England left back went under the knife last week to remove a piece of bone in his hip and is now recovering.
This leaves Chelsea without a recognised left back as Ashely Cole is still not fit.
Chelsea hope to have Ash available for the Community Shield on August 8.
Meanwhile Chelsea are playing a cat and mouse game with three players' contracts; John Terry, Frank Lampard and Arjen Robben.
All three have two years left on their current deals and now is the time to start talks on new ones.
It would be a disaster for Chelsea if the deals went sour and all three refused to sign again.
It would allow Robben to go to Real Madrid, Lampard to Barcelona and all the world's top teams would clamber for the England skipper's signature.
Chelsea are banking on the Englishmen's loyalty to Chelsea, but in this day and age,where agents have no sentimental feelings, Chelsea could be rocked to their foundations by the loss of Terry and Lampard.
Chelsea have already covered for the loss of Robben wih the signing of Malouda.
Didier Drogba has intimated that this could be his last season at Stamford Bridge.
The Ivory Coast striker wants to expand his playing experience and a successful season will see him land a spot at either of the top Spanish or Italian giants the season after this one.
With the future of Andriy Shevchenko still unclear, Chelsea will have to start soon to find replacements for their number one and two strikers.