After the successful appeal against their transfer ban, Chelsea are now clear to work the January market.
And Sport-Express says Chalov, a favourite of Blues owner Roman Abramovich, is on Chelsea's shopping list.
The Russia international is being considered as a replacement for Oivier Giroud, who wishes to leave next month in search for regular football.
Chalov has a deal with CSKA to 2022 and in 25 games this season has scored six goals and produced five assists. He was also the subject of an offer from Crystal Palace last summer.