Sun Sport had revealed in March this year that coach Guus Hiddink had recommended the 25 year old, dubbed the Russian Ronaldinho, to Blues owner Roman Abramovich.
Zhirkov's agent yesterday claimed a four-year deal was signed two days ago and that the CSKA Moscow star will move to Stamford Bridge later this summer.
The left winger, who can also play at left-back, has yet to complete a medical.
And while the details of the contract have been agreed, it has not yet been signed.
Under Hiddink's advice, Chelsea will look to clear out several players this summer - including Florent Malouda and Salomon Kalou. (ANI)