The right-back has become one of the most in demand players in the Football League, and he seems likely to leave Elland Road in the imminent future.
Leeds chairman Massimo Cellino has already stated that he is looking to sell Byram, and he reportedly will accept offers of around £5 million.
The 22-year-old has just six months left on his contract, and he has rejected all of Leeds’ offers of a new deal.
Byram is said to be keen on a move to Everton, who are still the front runners to sign him, but West Brom are also hopeful of wrapping up the transfer.
The Baggies are in a comfortable position of mid-table in the Premier League, and they have money to invest in January, given that their top flight status looks very secure.
West Brom have been forced to start players out of position at full-back this season, and Tony Pulis is eager to bring in some defensive recruits in January, to increase his options.