Guus Hiddink's shock announcement this week of his decision to retire came out of the blue for Anzhi.
But the 66-year-old, who has managed Real Madrid and Chelsea, did admit that a run at the Champions League with Anzhi next season could tempt him to stay on a year longer.
The Dagestan club, which has Samuel Eto'o in attack, is second, three points behind CSKA, after 17 games and Hiddink's hint has left the Anzhi players knowing what they have to do to change his mind.
"CSKA are a strong squad, which has already clinched success at domestic and European level," the former Socceroos mentor said.
"And they lead the league deservedly.
"Anzhi also topped the table not so long ago but we failed to stay there for a long time. And we have plenty of work to do to move to the top again."
CSKA will again be without injured forwards Seydou Doumbia and Tomas Necid as well as Chilean winger Marc Gonzalez.
Champion Zenit St Petersburg, which is experiencing a difficult time after being handed a technical defeat for its fans' unruly behaviour in the away match with Dynamo Moscow, will face another Moscow club, Spartak.
The old rivals represented Russia in the Champions League but both have dropped out after the group stage.
Spartak, meanwhile, sacked Spanish manager Unai Emery this week after a 5-1 thrashing at the hands of city rival Dynamo.
General manager Valery Karpin, who led Spartak to the runners-up spot last season, took over the nine-time Russian champion again as an interim coach.
Spartak will be without skipper Sergei Parshivlyuk, Irish midfielder Aiden McGeady and goalkeeper Artem Rebrov.
Wing back Yevgeny Makeev is also uncertain for the match after suffering a minor knee injury against Dynamo.
Zenit has ordered 5000 tickets for its fans, who will have to submit valid passport details to secure a place in the ground in an attempt to avoid a repetition of the crowd trouble which cost the club three points against Dynamo.
Dynamo, which is showing serious progress under Romanian manager Dan Petrescu, takes on Rubin Kazan in a match to be played behind closed doors.
Dynamo's Russian international striker, Alexander Kokorin, is doubtful after suffering a minor injury in the match with Spartak.