On-loan at Stoke from PSG, Jese came close to leaving the Potters in January for his hometown club.
He told Marca: "There were conversations, but the reality is that I continue to talk to (president) Miguel Ángel Ramírez, who is a good friend and knows that I have difficulties in the team where I currently play.
"There was also the theme of the child. I preferred to stay with him, taking care of my son."
Jese has been back and forth between England and Spain to take care of his prematurely born son.