A prosecutor says he did not declare income from the use of his image rights in order to get an "illicit benefit".
The claims against Mourinho come amid a lengthening list of tax fraud cases involving soccer stars in Spain.
Ronaldo, who is in Russian Federation at the Confederations Cup with Portugal's national soccer team, has played in Spain for Real Madrid since 2009.
Both Ronaldo and Mourinho are represented by Portuguese agent Jorge Mendes.
Real Madrid player Cristiano Ronaldo has been called to testify on July 31 in Madrid on allegations that he hid income from tax authorities between 2011 and 2014, according to a report in El Confidencial newspaper on Tuesday.
Mourinho guided Real Madrid to the 2011-12 LaLiga title, returning to manage Chelsea after leaving the Bernabeu in June 2013 before taking over as Manchester United boss last summer. The Portuguese worldwide is set to give evidence in his case on 31 July.
Ronaldo, 32, has denied the charges and is threatening to leave Spain after running into problems with tax authorities.
The accusations against Ronaldo have caused speculation in Portugal and Spain that he is now considering leaving the country to play elsewhere. The Madrid prosecutor says the case was presented to a local court.
Neymar, his father, and Javier Mascherano have also had their troubles with tax over the last couple of years.