The former Arsenal star would join the Reds on a free transfer after being released by Manchester City.
Clichy, 31, spent six years at the Etihad after joining from the Gunners for £7m.
And according to The Sun, Liverpool want the former France star.
They say Clichy is now contemplating Liverpool's offer - which would last until 2019 with a one-year extension option.
The Reds are in desperate need of a left-back this summer.
Jurgen Klopp has played James Milner in the position after axing Alberto Moreno midway through the campaign.
Clichy could replace Milner in his makeshift position in Klopp's back four.
The Sun add that Paris St-Germain are also eyeing the left-back.
Should Liverpool land Clichy, he would be their second signing of the summer.
Chelsea ace Dominic Solanke joined the Reds today and will complete his move on July 1 when the transfer window opens.
