The Uruguayan has struggled to force his way in the Reds’ first-team this season, and could be allowed to leave on a temporary basis to gain experience.
He is currently fourth choice under manager Brendan Rodgers, with his regular defensive pairing of Daniel Agger and Martin Skrtel backed up by veteran Jamie Carragher.
The Baggies are hopeful that they can use this to bring him in for the rest of the season with a view to a permanent move during the summer.
With Jonas Olsson attracting the interest of QPR, and having a £4m release clause which will be active during the summer, Steve Clarke is aware that he must plan for the Swede’s eventual departure.
He sees Coates as the ideal man to step in at the Hawthorns, after coaching him at Liverpool, and is believed to be prepared to make a move within the next 48 hours.
The 22-year-old arrived at the club last season in a big money move from Nacional is his homeland.
He has featured sporadically this term, managing only a handful of Premier League appearances, including a full 90 minutes against Manchester City.
The bulk of his game time has come in the Europa League and Capital One Cup.
Liverpool still value the centre-half highly, and may be unwilling to allow him to leave on a permanent deal.