Senegal international Kamara, who signed a three-year deal last summer with a year’s option in the club’s favour, has been told he will only be allowed to leave if the Baggies receive an offer they cannot refuse.
Kamara finished last season as Albion’s 23-goal top scorer and made the PFA Championship team of the year.
But manger Tony Mowbray, who last week rejected a transfer request from defender Curtis Davies, said: “I am disappointed to receive a transfer request from Diomansy because I enjoyed working with him so much last season.
“We would need a head-turning offer before we even consider letting him go.”
Chairman Jeremy Peace added: “We have made our position quite clear. None of our players will leave unless we receive offers which are too good to turn down and the deal suits this club.”