Albion chairman Jeremy Peace has insisted he will not sell any of the club's star players unless he receives a 'head-turning' offer this summer.
And having already rejected big-money bids for both Jason Koumas and Diomansy Kamara, Peace appears to be keeping his word.
Koumas and Kamara have both expressed a desire to play in the top flight following West Brom's failure to win promotion last season.
And on Thursday highly-rated centre-back Davies had a transfer request turned down by the Baggies, who signed the 22-year-old for £3million from Luton two seasons ago.
Albion boss Tony Mowbray does not want to keep players who do not want to play for the club - but will not just "let players walk away".
Peace is believed to have turned down an £8.5million bid for Davies from Portsmouth last summer - and this time around would only accept an offer in the region of £10million for a player widely tipped for full England honours in coming seasons.
London rivals Arsenal and Tottenham have been heavily linked with Davies, while Wigan also had a bid for him rejected last summer.