The 32-year-old is understood to be unhappy with what he perceives as a lack of protection from the club after he was charged with defrauding the Spanish government of £13m in unpaid tax.
Mourinho was Real Madrid coach from 2010-13.
Facebook/CristianoRonaldo has expressed his desire to transfer back to Manchester United.
The cases are about the profits made from image rights, not salaries from their clubs.
"I want to talk with him", the long-serving Real president said.
For example, tax on any earnings in 2012 could be paid as late June 30, 2013 which would also enable the Spanish tax authorities to look back that far in their records for what they consider to be more potential breaches.
This morning (Thursday) SunSport reported how CR7 was being "persuaded by his lawyers" to pay the bill that is being chased by the Spanish tax authorities.
A statement released by Gestifute read, "Jose Mourinho has not received any notification with regards to the news published today".
A host of football stars have run into trouble in Spain over suspected tax fraud related to image rights, with Madrid forward Cristiano Ronaldo summoned to appear in court on July 31 to answer four counts of tax evasion of 14.7 million euros.
The guilty pleas of Di Maria, Mascherano and Messi, however, would suggest this is not always the case and Mourinho and Ronaldo will need to be certain the offshore companies they set up to receive their image-rights payments are entirely legitimate.
The accusations against Ronaldo have caused speculation in Portugal and Spain that he is considering leaving the country to play elsewhere.
Amid swirling reports that Ronaldo wants to leave Real Madrid and return to Manchester United, comes a fresh report from Spain's Marca that Mourinho is not in favor of a big-money move to sign the reigning Ballon d'Or victor.
It will be up to a judge to decide whether to take Mourinho to court.
However, Di Maria is unlikely to serve time behind bars as a sentence under two years for non-violent crime can be served as probation, according to the Spanish law.