The Japan international's contract with the Russian outfit expires in December and AC Milan are reportedly one of several top European clubs ready to pounce
The Japan international is out of contract at the end of the year and has been heavily linked with a move away from the Russian capital, with AC Milan said to be leading the chase for the playmaker's signature.
However, Slutsky insists he is unaware of any concrete interest in Honda and hopes to keep hold of one of his team's star performers.
"What I can say is that Honda is still our player today," the CSKA boss told Tuttomercatoweb.com. "But his future doesn't depend on me, and I cannot say if he will stay or not. That is something for the club to deal with.
"I can only say that Honda is a fantastic footballer, but I don't really know who is following him.
"Can I see him doing well in Italy? I could see him doing better in the Champions League, in a CSKA jersey!"
The 27-year-old Honda, who caught the eye during his country's brief Confederations Cup campaign, joined CSKA from Dutch outfit VVV-Venlo in 2010.