The 33-year-old revealed on Monday night that he expects to find a new team for next season after spending eight years at Stamford Bridge.
Redknapp believes that the former England international could be able to revive his career at Anfield.
"Off the top of my head, Liverpool probably need a left-back," the former Reds midfielder told Sky Sports News. "Jose Enrique was injured for large parts of the season and they've played Jon Flanagan at left-back and Glen Johnson at left-back at times.
"Brendan Rodgers knows him well from his time at Chelsea so that might happen."
Cole made 26 appearances in all competitions for Chelsea during the 2013-14 campaign.