The 26-year-old, who impressed greatly with his country during the 2010 World Cup in South Africa, has gone on to enjoy success in the Russian league and European football with his current club.
However, after initially looking set to pen a new deal with CSKA Moscow, negotiations have since broken down and Honda will now depart on a Bosman free transfer when his current contract expires at the end of the season.
CSKA director Roman Babaev said: "We tried to extend his contract, but we can't force him.
"It is up to him what happens next."
The recent events have paved the way clear for other clubs to come in with an offer and reports claim Liverpool boss Brendan Rodgers will look to tie him down to a pre-contract agreement in the near future.
Honda would then battle it out with the likes of Luis Suarez and Daniel Sturridge for a place in the starting XI at Anfield next season, while it would surely end Andy Carroll's spell on Merseyside.