Versatile Zhirkov, who tends to play left-back for Russia, said: "Clearly we are talking about one of the best clubs in the world, who regularly compete at the highest level.
"It is very possible I would say yes (to Chelsea). But before that I would have to weigh up the pros and cons.
"To sit on the bench and only get on the pitch from time to time doesn't interest me, not even at Chelsea.
"Moreover, I have nothing to lose (by staying in Moscow), given that CSKA now have a very interesting team who will begin competing in the Champions League in the autumn."