Punto Pelota says the pair met last week to discuss Mourinho's situation and Perez made it clear he wants his coach to continue next season.
Mourinho insists he's not signed any contract with any club, though remains undecided over whether he will remain in Madrid.
Perez understands Mourinho's position, knowing he has been hurt by the treatment from the Madrid media this season and his battles with the locker room.
But there is a growing feeling inside the Real boardroom that Mourinho is leaning towards staying.
Can Florentino's charm offensive convince Mou? Give us your shout below...