Newcastle are believed to be open to selling the striker, who struggled for goals in the Premier League last season, although with Stoke's opening offering being less than what the 'Magpies' paid for Gayle, they may have to up their bid.
Gary Rowett wants to pair the striker with Benik Afobe, and Andre Gray is another name linked with the club.
Gayle was prolific for Newcastle during their season in the Championship, netting 25 times as they romped to the league title.
Additionally, Gayle may not be the only exit from St James' Park, with Chancel Mbemba discussing a move to Porto.