Birmingham City are thought to have slapped a £12m price tag on the 22-year-old, who has scored eight times in 17 Championship appearances this season.
Stoke boss Gary Rowett signed Adams from Sheffield United in 2016 while he was Birmingham manager, and also tried to bring him in while manager of Derby County.
With Adams targeted as the player to help boost Stoke's promotion chances, the 'Potters' are expected to open the bidding at around £5m although Garry Monk will be reluctant to sell for such a price.
The 'Blues' rejected a £10m bid from Fulham in the summer for Adams, who had over three seasons left on his contract.