The midfielder has just entered the final year of his contract with Russian outfit and it is thought that he could be tempted by a Premier League move.
He has been long linked with a move away from CSKA, and came close to completing a switch to Lazio during the summer.
The Japanese midfielder’s performances this season have been openly criticised by his manager Leonid Slutsky, leading many to believe that he could consider his options.
Brendan Rodgers is thought to be keen to draft in a long-term replacement for ageing skipper Steven Gerrard and sees Honda as the ideal candidate.
The playmaker was one of the stars of the 2010 World Cup in South Africa helping Japan reach the knockout stages.
He was also voted as player of the tournament during the Asian Championships last year.
Honda shot to fame with Dutch side VVV-Venlo after an impressive spell at the club between 2008 and 2010.
This tempted CSKA Moscow to part with a fee believed to be in the region of £5m for the midfielder.
It’s thought that they will now accept a figure in the region of £12m for him rather than risk losing him on a free when his deal expires.