Perez is confident the pair can work together.
"There has been an importance placed on this (rift) that has not matched the truth," he told AS.
"It is true that Mourinho demanded more autonomy and that seemed fine to Valdano and me.
"Today for example, we have traveled together because Mourinho has never asked not to travel with the team. Everyone respects their work and both are necessary and compatible.
"Mourinho is zealous in his work but does almost everything well and has the values of Madrid."