Skysports.com understands West Brom have received three bids for Jerome Thomas and have rejected them all.
Fulham, Queens Park Rangers and West Ham are the sides believed to have tabled offers for the winger.
The Baggies are reluctant to do business, though, as Thomas remains a key part of their plans.
The 28-year-old has only recently shaken off a hip problem that has delayed his start to the new season.
He made his first appearance of the campaign in the Baggies' 4-1 Carling Cup victory over Bournemouth, and opened the scoring after just seven minutes.
Roy Hodgson is now mulling over whether to hand Thomas his first Premier League start of the season against Stoke on Sunday.
The Baggies boss remains a big fan of the former Arsenal and Charlton man and is not prepared to discuss a sale during the summer transfer window.