A statement issued by the section for economic crimes of Madrid's provincial state prosecutor's office said its investigations indicated that Mourinho committed tax fraud in 2011 and 2012.
Ronaldo was last week accused of evading 14.7 million euros through offshore companies and will appear before a judge on July 31.
Portugal coach Santos, who guided the team to Euro 2016 glory a year ago, was asked whether Ronaldo's future had become an issue and if he believed he would still be a Real player next season.
Rio Ferdinand hopes Manchester United can complete a sensational deal to take Cristiano Ronaldo back to Old Trafford. The two overlapped at Real Madrid from 2010-2013, winning one La Liga title and a Copa del Rey.
The accusations against Mr Mourinho, now the manager of Manchester United, date back to his time as coach at Real Madrid.
Ronaldo's future at Real Madrid looked guaranteed after lifting his third Champions League title with the club earlier this month, the Portugal global scoring twice in a 4-1 win over Juventus.
The 32-year-old four-time World Footballer of the Year is alleged to have not paid the correct taxes from 2011 to 2014.
Outraged at being unfairly treated by Spanish tax authorities, Ronaldo had earlier expressed his intentions to leave Real Madrid C.F. and Spain.
"I haven't learned very much about the situation, he's at a very important tournament at the moment in the Confederations Cup and until that ends I'm not going to disturb the atmosphere of his team", Perez said. Mourinho left Real Madrid in the summer of 2013.
There has been speculation that Ronaldo is trying to put pressure on Real so that they will bear some of the burden of an eventual fine as Barcelona did for Lionel Messi.
Both were given 21-month jail sentences, though neither is expected to serve the time as it was a first offence and the sentence was under two years.
Former Barca defender Javier Mascherano also agreed a one-year suspended sentence with authorities for tax fraud last year.