On-loan from PSG, Jese is being linked with a move away from Stoke this month as his newly born baby recovers from complications.
Ramirez said on Wednesday: "Jesé is a player of Stoke City.
"It has been several weeks since he was not in England because of a personal problem for which I hope he finds a solution. From there, we will see what happens.
"He knows it's his home and if he wants to come back, the doors are open."