The Japan international has been linked with a number of clubs in the past few months, headed by Liverpool and Arsenal, but fresh reports suggest that La Liga outfit Atletico Madrid are showing considerable interest.
Honda's agent Kees Ploegsma is over in Qatar overseeing the interests of his client whilst he competes at the Asian Cup and revealed to reporters that the talented forward may be on his way to the Vicente Calderon Stadium if all goes smoothly with his Russian club.
"A number of clubs have expressed their interest," he said.
"At this stage, we are waiting for a serious offer. I'm really hoping that something can happen, but we'll have to wait and see.
"The most likely scenario for him at the moment is to remain at CSKA. If they are willing to let him go, Atletico Madrid could be an option.
"He wants to stamp his game on the Spanish style of play."