The Daily Telegraph says Dawson is a target for a number of Premier League clubs and West Ham have seen an opening offer rejected, with Albion understood to be rating the 28-year-old at more than £20 million.
He adds that Burnley have also had bids turned down for Dawson, one of the few consistent Albion players in the club’s relegation season, and West Ham are considering whether to make an improved offer.
Dawson can play at right-back or centre-half and Albion had hoped to persuade him to sign a new contract.
Whether West Ham, who are in the market for a second centre-back has made an official bid is unknown but the notion that Dawson is valued at £20m by the Baggies has been met by bewilderment by West Ham fans on social media.
What is also bewildering if there is anything in this story is that Manuel Pelegrini has turned down the chance of signing Alfie Mawson because he isn’t keen on signing various relegated players.