Morata is being heavily linked with a move away from the Bernabeu.
The 24-year-old struggled for regular game time under Zinedine Zidane last season, making just 14 starts in the Spanish top flight.
He was also only used as a last-minute substitute in their Champions League triumph over Juventus.
Starsport understand both Manchester United and Chelsea are keen to take Morata to the Premier League.
Sky Sports claim the Red Devils have already had a bid of £52.4m rejected by Real.
According to Diario Gol, Perez, the Spanish club's president, is seeking around £78m for the forward.
But Morata is reportedly pleading with the Bernabeu chief to lower his valuation so he can seal an exit.
Diario Gol say he believes Perez owes him a favour after he helped convince Isco join Real instead of Manchester City in 2013.
Real parted with more than £25m to re-sign Morata from Juventus last summer.
There are still four years left to run on his contract in the Spanish capital.
He ruled out a return to Italy with AC Milan after Saturday's final, saying: "Milan? No, I certainly won’t be in Italy.
"I want to continue here and it’s difficult.
"I can only tell you what I read in the papers, I know nothing else."
