Sources in Moscow say Stamford Bridge owner Roman Abramovich has held preliminary talks with the Russians over the 25-year-old's summer transfer, says the Daily Mail.
Zhirkov, who prefers to play down the left wing but can also fill in at left back, is considered one of the best wide men in the world by Russia and Chelsea boss Guus Hiddink and he possesses the pace sadly lacking in the Blues team.
Abramovich and Hiddink saw Zhirkov in action during CSKA's UEFA Cup victory against Aston Villa last month.
Zico said: "Zhirkov is a player of such high level that in my opinion he would show all his real potential only playing in such a strong competition as the English Premier League.
"He would easily fit into Chelsea's first-choice team. I don't like to lose him but I won't stop his move to London."