Real Madrid have accepted a £21m ($28m) bid from Paris Saint-Germain for striker Jese.
French newspaper L'Equipe reported that the transfer fee was agreed by the two clubs over the weekend, paving the way for personal terms to be discussed.
Real coach Zinedine Zidane had urged Jese to join another club if he wanted to play regular first-team football earlier this summer.
Alvaro Morata's return from Juventus has increased competition in the striking positions at the Santiago Bernabeu, with James Rodriguez, Isco and Marco Asensio all ahead of Jese in the pecking order.
Premier League clubs Arsenal and Liverpool were both linked with moves for the 23-year-old Spaniard.
La Liga outfit Espanyol were also interested in signing the forward, who has represented Spain through the U-16 to the U-21 levels.
Speaking at a news conference on 2 August, Zidane said Jese's move to PSG was not yet finalised.
"It's still not finished, but it's on the way," he was quoted as saying by Goal.
"Is PSG an ideal fit for him? I think so. He's going to score a lot of goals there. I hope it goes well for him there, but Madrid will always be his home."
Jese made 28 league appearances for Real Madrid last season, scoring five goals. He has 12 months left on his contract at the Bernabeu.
Arsenal striker search
Arsenal are in the market for a striker and have been linked with a move for Inter Milan captain Mauro Icardi.
The North London club have had a £29m (€35m) offer rejected for Lyon striker Alexandre Lacazette.
Sources told Sky Sports that the Gunners will follow up with an improved offer for the Frenchman in the coming days.
Lyon are reportedly holding out for a fee in the region of £40m, while the club's president Jean-Michel Aulas has insisted that the striker will not be sold this summer.