The 30-year-old starred for Newcastle before joining the Reds in 2011, where he was initially a first-team regular.
However, some erratic displays and serious injury set-backs over the course of the past couple of years saw his stock drop to an all-time low, and the Merseysiders opted against keeping him on when his latest contract expired at the end of last season.
Now available on a free transfer, Enrique has a list of suitors monitoring his situation, with reports claiming that Palace and West Ham, as well as West Brom, are among them.
The Hammers are shopping for a new left-back after Aaron Cresswell suffered a nasty knee injury in pre-season action, while Eagles chief Alan Pardew coached the Spaniard during their time together at Newcastle.
However, the interested Premier League sides face competition from the player’s homeland, where Espanyol and Malaga are keen.