Football League World report that the Hornets are asking for £15m for his services and the Potters are interested, as new boss Gary Rowett continues his search to strengthen Stoke's attacking options ahead of a season in the Championship, having already brought in Benik Afobe from Wolves.
Stoke are expected to have a major overhaul of the current squad, with many of the current first team players expected to leave the club this summer.
Gray, 26, arrived at Watford from Burnley just last year, but has struggled to make an impact at the club, managing just five goals in 31 Premier League appearances last season.
However, the Englishman has a prolific record in the Football League.
Gray scored 18 goals for Brentford during the 2014/15 campaign, earning himself a move to then-Championship Burnley where he scored 25 goals during the 2015/16 campaign, spearheading the club's promotion to the Premier League.
Gray's acquisition would give Stoke a strong boost in their aim to bounce back to the Premier League at the first attempt, so a £15m price tag may be viewed as a very tempting and worthwhile investment.
Gayle was prolific in the second tier despite an injury spell during the season, scoring 23 goals in 34 appearances during Newcastle's 2016/17 spell in the Championship.
The forward has failed to score anywhere near as regularly in the Premier League for the Magpies and could leave St. James' Park this summer.
Similarly to Gray, Gayle would offer Stoke a significant boost in the push for promotion and is a cheaper option to the Watford man.
However, Newcastle boss Rafa Benitez is unlikely to allow Gayle to leave without signing a replacement first.