The complicated structure used by Mr Mourinho also incorporated two Dublin-registered companies registered to the north inner city address of Moore Stephens accountants.
Spanish authorities have also recently filed papers against Real Madrid star Cristiano Ronaldo, who is accused of evading tax of some 14.7m euros (£12.8m) by hiding income from image rights.
Ronaldo's future at Real Madrid looked guaranteed after lifting his third Champions League title with the club earlier this month, the Portugal worldwide scoring twice in a 4-1 win over Juventus.
Prosecutors said he had failed to declare revenues from his image rights in his Spanish income tax declarations from 2011 and 2012, "with the aim of obtaining illicit profits".
Di Maria is, like Ronaldo and Mourinho, a client of the Portuguese super agent Jorge Mendes, who himself has been summoned to appear before the court at Pozuelo de Alarcon, just outside Madrid, on June 27.
Ronaldo and Mourinho are the latest members of the soccer elite to be accused of tax fraud in Spain.
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But tax authorities later found that some of the information presented in that settlement was incorrect, the prosecutors said.
Mourinho's management team - Gestifute - and Real Madrid did not immediately respond to CNN's request for comment.
The Portugal forward has strenuously denied the allegations and threatened to quit the country.
Despite being handed a 16-month sentence, Di Maria will not go to prison as is normal in Spain for first offences for non-violent crimes carrying a sentence of less than two years.
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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