The 24-year-old joined PSG from Real Madrid last summer in a deal worth £22m, but failed to live up to his price tag under Unai Emery and was sent on loan to Las Palmas in January.
Jese appeared close to a move to Fiorentina earlier in the window, but Mark Hughes looks to have snapped up a deal for the player who once showed so much potential at the Bernabeu.
The Spaniard had a medical at Stoke on Monday morning and the club are now poised to announce the signing of the forward.