Mepham was known to be interesting Eddie Howe's side in January, with this now the second time that the 'Bees' have held firm in their valuation of the player.
With the player still having four years remaining on his contract, Brentford are under absolutely no obligaiton to sell and the club have shown in the past that they will only do so when their valuation is matched.
Aged just 20, Mepham is considered to be one of the most exciting defensive prospects in the Championship and made 21 appearances in all competitions last season.
Bournemouth have money to spend after selling Benik Afobe to Wolves, with Howe thought to be focusing on reinforcing his back four this summer.