The 29-year-old full-back has struggled with injuries in recent seasons and made just two Premier League starts last term with Brendan Rodgers using fellow Spaniard Alberto Moreno as his first-choice left-back.
Pulis has already lured one Liverpool player to the Hawthorns this summer, with forward Rickie Lambert leaving Anfield earlier in the transfer window, and will look to repeat the trick with former Newcastle United man Enrique.
The Spaniard hasn’t come close to the form that he showed during his time at St James’ Park and has fallen down Brendan Rodgers’s pecking order, with youngster Jon Flanagan also set to return from his spell out with a long-term knee injury.
Enrique features only four times in the EPL last term, of which only two appearances were starts, while he managed a meagre eight appearances the year before. At Newcastle, by contrast, he was a near-ever-present, managing 36 outings in his final season in the north-east-the 2010/11 campaign.
The Daily Star states that Pulis is looking at a number of potential defensive additions, with Tottenham’s Federico Fazio said to be on his West Brom wish-list and Swede Jonas Olsson understood to be on his way out from the Midlands side.
West Brom conceded 51 goals in Premier League action last season and Pulis will be keen to keep things tighter at the back in 2015/16. The Throstles begin their Premier League campaign against Manchester City on Monday evening in the last of the opening weekend’s fixtures.