David Woods writes in The Daily Star that manager Brendan Rodgers "is a big fan of the left-back Cole, who he knows from his time at Chelsea" and claims that "Cole is understood to be interested in the move to Anfield."
The 33-year-old would be a surprise signing, and his age brings with it both positives and negatives. It means he certainly wouldn't be a long-term solution, nor would he seemingly be capable of playing every game domestically and in Europe.
But Cole would bring with him vast experience, especially when it comes to winning major trophies, something that could benefit Liverpool's youthful squad.
It's possible that Rodgers may be looking at Cole as an addition to the squad, rather than as a first-choice player, looking to sign a younger left-back this summer too. Alternatively, much of these reports linking Cole to Anfield could be fed through the player's agent as he seeks a final big money move.
Either way, as discussed, Cole is not the long-term solution, so here are some other options that Liverpool could realistically target this summer.