New Potters boss Rowett is holding a transfer summit early this week to step up his spending plans.
MirrorSport understands he is pushing to buy Newcastle hitman Gayle and Wolves frontman Afobe.
Gayle, 27, scored 23 goals in 2016/2017 to help the Toon back to the Premier League to justify his £10million fee.
While Afobe, 25, scored six goals for Wolves last season after arriving in January on loan from Bournemouth.
Promoted Wanderers have since snapped Afobe up permanently but Stoke believe they persuade them to already part with him for around £12m-£14m.