They said Mourinho had already settled a previous claim relating to his Spanish taxes, which resulted in a penalty of 1.15 million euros in 2014.
Both Ronaldo and Mourinho are represented by agent Mendes, who will act to act as a peacemaker.
Speaking about Ronaldo's reported desire to leave the club, Perez added: 'Not I, nor anyone at Madrid, is contemplating that Cristiano could leave the club'. Real Madrid and Man United are not directly involved.
Mourinho was Real Madrid coach from 2010-13.
Now, the admission of the two counts of fraud in 2012 and 2013 will see him pay an additional fine of nearly 780,000 euros.
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Cristiano Ronaldo remained silent on his Real Madrid future after taking no questions during a postmatch news conference following his Man of the Match award in the wake of Portugal's 1-0 Confederations Cup victory against Russian Federation in Moscow.
Media consortium European Investigative Collaborations (EIC) has claimed that no less than 185 million euros worth of income has escaped the attentions of tax authorities using shell companies and offshore accounts.
A prosecutor said Mr Mourinho, 54, did not declare income from image rights in order to get an "illicit benefit".
Manchester United and Paris St Germain have been alerted to Ronaldo's potential availability following the revelations of his disenchantment with his predicament in Spain, but his former club have played down talk of a return to Old Trafford. Under Spanish law, a first-time offender is not required to serve time in jail for a sentence below two years.
Mascherano was also convicted of tax fraud last year and was given a suspended one-year sentence.
He has reportedly made a deal with Spanish authorities to avoid a Supreme Court trial, which found his fellow Argentina captain Lionel Messi guilty of tax evasion, sentencing the Barcelona forward to 21 months in prison.
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