Cole has struggled to force his way back into the Liverpool team since he returned from a season-long loan at French side Lille.
The 31-year-old made 32 appearances for the Ligue 1 club and scored four goals.
Should Cole choose to link up with Redknapp it would not be for the first time. The former England international played under Redknapp during his time at West Ham.
The midfielder scored his first goal of the season against the Hammers last week, but doesn't appear to be in Brendan Rodgers' plans.
Meanwhile, QPR are preparing an official approach for Tottenham coach Les Ferdinand.
They are also keen on adding Clive Allen to their set-up. Mail