The Blancos president believes the outgoing coach suffered "personal abuse" from some quarters while in charge at the Santiago Bernabeu
The Portuguese has parted ways with the Liga giants after three years at helm following a trophyless season which saw him reportedly fall out with a number of high-profile players and have swathes of fans get frustrated with him.
Following Madrid's 4-2 win over Osasuna in Mourinho's final game on the Santiago Bernabeu sidelines, Perez believes extreme pressure forced the Chelsea-bound coach out but suggested he could return someday.
"The door isn't closed to him," the club chief told ABC on Sunday. "He’s sad to leave, it’s hard for him to understand the media here.
"It’s not easy to live with the pressure, which at times has been unfair, bordering on personal abuse. It is difficult for people to understand that football is like that in Spain.
"In the end we reached the conclusion that, for everything, after three years, the best thing for him and for the club is to part company and remain good friends. Life is long and nobody knows what might happen."
Perez went on to admit he admires Paris Saint-Germain coach Carlo Ancelotti but refused to name who his choice is to be Mourinho's successor.
"[Ancelotti's] a fantastic coach, but he’s got a contract with his current club, which we respect," he added.
"The club needs a coach who understands the club well and can bring in some players to improve the team, not many though."