The 27-year-old Japan international has been linked with some of the biggest names in European football, including most recently AC Milan. Liverpool, Arsenal and Everton were the three Premier League teams mentioned with an interest in the playmaker.
His CSKA Moscow contract expires during the January transfer window, and Honda has confirmed he has no intention of signing a new deal.
"I have many choices, but I want to compare as much as possible," said Honda. "I don't think there's a chance I will stay in Russia.
"I just need to focus on the Russian league and the Champions League, so I don't want to talk about this right now."
Arsenal signed Mesut Ozil in a £42.5m deadline day signing, so the Gunners may not be interested in Honda when his contract runs out in four months time.
Liverpool, on the other hand, missed out on Willian to Chelsea and are believed to be still on the lookout for a new attacking midfielder.
Brendan Rodgers signed Luis Alberto and Iago Aspas over the summer window, while Coutinho - a January capture from Inter Milan - has impressed for the Reds.
But the opportunity to sign Honda, a player with top Champions League experience, could be too good to pass up for the Anfield boss.