Current Madrid boss Rafael Benitez is under pressure at the Spanish club having suffered an indifferent start to the campaign.
Mourinho, who was recently sacked by Chelsea, managed Madrid between 2010 and 2013 but famously fell out with a number of players during his time in La Liga.
However, Perez has sounded out directors and influential club members over the possibility of bringing him back to Madrid.
Man United are reportedly interested in Mourinho should they sack the under pressure Louis van Gaal.
The majority of fans thought the Dutchman would be let go following the 2-1 defeat against Norwich City, which meant United extended their winless run to six games.
However, van Gaal has reportedly been given the next two matches against Stoke City and Chelsea to save his job. The hope for fans is that the decision does not back fire and Mourinho goes elsewhere before United get a chance to bring him in.