Various reports suggest that the Japan international is again on the radar of the Reds who have been credited with an interest in his services in the past.
According to CSKA director Roman Babaev, Honda looks likely to leave Moscow in the summer.
"We tried to extend his contract, but we can't force him," Babaev said.
"It is up to him what happens next."
It is believed that Liverpool are looking to clinch Honda on a pre-contract agreement ahead of a shift to Anfield at the end of the current campaign when his CSKA contract expires.