Coventry City managed to hold on to Gyokeres despite Premier League interest in the January transfer window.
But their failure to win the Championship playoff final means the forward is likely to move on from the club this summer.
There is considerable Premier League interest him, with clubs such as Everton and West Ham believed to be keen on the forward, who scored 21 times in the Championship last season.
Wolves also have a genuine interest in Gyokeres but the striker is unlikely to end up at Molineux for the moment.
The budget is tight due to Wolves’ commitment to FFP regulations and they will not be spending big this summer.
Julen Lopetegui wants to sign a striker and Gyokeres is a player the Wolves recruitment team like.
But the club will stay away from big-money deals this summer and Coventry are likely to ask for a considerable fee for the striker.