United are hopeful their transfer embargo will be lifted ahead of the summer after the return as chairman of owner Massimo Cellino.
Neil Redfearn has put forward an ambitious list of potential targets to Cellino, which also includes Burnley defender Jason Shackell and QPR winger Matt Phillips.
Adam has scored three goals in his last five games for Stoke but has not been a regular starter.
The 29-year-old deep-lying playmaker has made 14 of his 26 Premier League appearances from the substitutes' bench.
Stoke are also looking to add another midfielder to their squad during the summer.