The talented forward has been linked with a loan move to Villa Park.
The 22-year-old is being linked with a move to Villa by Spanish source Punto Pelota. The Real star is highly rated in the Spanish capital but has recently seen his playing time battered by injury and competition for places.
He suffered a serious knee injury in March 2014 which kept him out of action for most of the year.
Now he has a fight on his hands to get ahead of the strikers at the Champions League winners, with Cristiano Ronaldo, Karim Benzema, Javier Hernandez and Gareth Bale all ahead in the pecking order.
Aston Villa could certainly do with some more attacking talent, but a loan move for Jese would come as something of a surprise.
The club have one Spanish talent at the moment in Carles Gil who cannot buy a game and Jese is a similar style of player to Gabriel Agbonlahor - with Tim Sherwood unlikely to hold back any homegrown players for someone borrowed from Spain.
This transfer rumour will struggle to stand the test of time.