The 28-year-old has struggled to settle at Stamford Bridge since his move from CSKA Moscow two years ago.
The left-sided Russian international has failed to displace Ashley Cole in the Chelsea team and he could make a £13m return to his native country.
"Of course, Yuri is a great player. Everybody in the team is very glad that he will join our club," said Anzhi Makhachkala defender Rasim Tagirbekov.
"This transfer will strengthen Anzhi a lot. Zhirkov has already managed to talk to the team's head coach Gadzhi Gadzhiev and practically all the players."
If Zhirkov does leave Stamford Bridge, it would allow Chelsea to bring an additional foreign player into their 25-man Premier League squad.
Zhirkov has scored one goal in 29 appearances during his two years at Chelsea.