The 27-year old has only made 49 appearances for the club since his £18 million move from CSKA Moscow two summers ago and has struggled to hold down a regular first-team place.
The player has been most heavily linked with a return to his homeland.
The player was signed on the recommendation of Guus Hiddink who coached the Russian national side for four years. But, with Hiddink linked with a return to Stamford Bridge he could be keen to keep the player.
Zhirkov has played in a variety of positions on the left for Chelsea but has struggled to dislodge Ashley Cole, Florent Malouda and Nicolas Anelka for most of the past season.