West Bromwich Albion are reportedly keen to sign a left-back in January.
West Brom are on the hunt for full-backs in January and Enrique has been touted as a potential addition.
The Spaniard proved his Premier League class while playing for Newcastle United, but he has fallen down the pecking order at Liverpool in recent years.
Alberto Moreno has become the Reds' first choice left-back, leaving Enrique on the sidelines.
The 29-year-old has not played once for Liverpool this term, and it does not seem likely that he will break into Jurgen Klopp’s team any time soon.
As a result, it seems that Enrique could be available in the new year, with West Brom reportedly willing to give him a fresh start.
Pulis has been forced to play Chris Brunt at left-back so far this season, and while the Northern Ireland international has been solid he is more comfortable in a midfield position.
A move to The Hawthorns could be just what Enrique needs to rejuvenate his career, but only time will tell if this one proves to anything more than just another rumour.