The attacker has only played in six league games for Sean Dyche's side this season.
He is available on loan and the two Championship clubs are very eager to sign him, per Football League World.
The 27-year-old wants a chance to play for the Czech Republic at Euro 2020 and knows he must be a regular to get in the squad.
It is likely that Burnley will give in to his wishes to leave so that he can get regular first team action.
West Brom would be the more appealing move for the player, as they are near the top of the Championship and likely to win promotion to the Premier League next season.