Club general director Roman Babaev is aware of interest from AC Milan for the Japan international, while Everton have also been linked with a move.
But as it stands, Honda, whose contract expires in January 2014, will remain a CSKA player until a club makes a formal approach for his services.
Babaev told Russian newspaper Sport Express: "[The situation] has not changed. Honda could be speaking to another club at the moment, because the rules allow it.
"But our position is clear. We are ready to let him go if we receive a reasonable offer.
"We are pleased that Milan are interested but we also have to be realistic. Yes, his expiring contract affects his market value but there is a limit as to how low we can go.
"We are not worried if he ends up leaving the club on a free transfer.
"It is a difficult decision to make - part ways with Honda now or keep him until his contract expires.
"We are interested to know how this progresses. The ball is in Milan's court now."