Evans has a clause in his contract that will allow the 30-year-old to leave The Hawthorns for just £3 million at the end of the season, according to the Mirror, and the Hammers are one of the teams - along with the likes of Everton and Leicester - interested in exploiting the clause.
Given Evans' experience and quality, it would be a major surprise if most of the teams in the Premier League were not planning a summer bid - so West Ham could certainly be forgiven for plotting a move despite already having a number of centre-back options.
And if West Brom do go down, and West Ham then win the race for Evans' signature, questions will surely have to be asked about what is left for James Collins at the London Stadium.
Collins has been a brilliant servant for the Irons across two spells, but transfermarkt reports that he is out of contract with the club this summer. And at 34 - 35 by the time the season ends - the presence of another experienced option may make the Welshman quite redundant as far as David Moyes is concerned.
It would certainly be a surprise if they offered Collins a new deal if they managed to land Evans and considering the options that they already have at their disposal and coming through the ranks, so perhaps the West Ham stalwart would be forgiven for monitoring West Brom's situation as closely as his club's board seemingly plan to.