The Manchester United boss is alleged to have been helped by advisers to avoid paying tax on earnings from the use of his image rights for product endorsement - an accusation that is strongly denied.
The claims emerged in a huge data leak of more than 18 million documents, probed for the past number of months by a group of media organisations including The Sunday Times.
Real Madrid player Cristiano Ronaldo is another high-profile name mentioned in reports as having allegedly moved money to a tax haven in the British Virgin Islands in what the newspaper described as “highly aggressive tax avoidance”.
The paper said it had found evidence suggesting tax officials in Britain and Spain had been misled by Mourinho’s advisers during a probe into more than £10 million apparently hidden in a tax haven.
The evidence has prompted calls for a criminal investigation into Mourinho’s tax affairs.
MP Meg Hillier, chairwoman of the public accounts committee, said: “These revelations are extraordinary and warrant a close examination by the UK tax authorities.”
Meanwhile the paper said Julian Lopez Milla of the Spanish parliament’s tax committee called for the case into his taxes their to be reopened to “investigate whether Mourinho has committed the criminal offence of tax fraud”.
Gestifute, which provides “career management” for sporting professionals, has rejected the allegations.
In a statement the firm, founded by agent Jorge Mendes, said: “One newspaper makes the unfounded allegation that Gestifute, its clients and its advisers of having, directly or indirectly, created, organised or designed tax structures to facilitate tax evasion using tax havens. The most serious and malicious allegations in the inquiries relate to José Mourinho and Cristiano Ronaldo.
It added: “Both Cristiano Ronaldo and José Mourinho are fully compliant with their tax obligations with the Spanish and British tax authorities.
“Neither Cristiano Ronaldo nor Jose Mourinho have ever been involved in legal proceedings regarding the commission of a tax offence.
“Any insinuation or accusation made to Cristiano Ronaldo or José Mourinho over the commission of a tax offence will be reported to the legal authorities and prosecuted.”
The European Investigative Collaborations (EIC) consortium - which worked alongside Germany’s Der Spiegel to which the information was originally passed from whistleblowing outlet Football Leaks, and other publications - said the documents uncovered in the leak include photographs, spreadsheets and emails.
It added that more revelations will be published in the coming weeks, giving “an unprecedented look into the gloomy depths of the modern football industry”, the Press Association reported.
An HMRC spokesman said: “HMRC carefully scrutinises the arrangements between football clubs and their employees in respect of any image right payments to make sure the right tax is paid – in recent years we have identified more than £80m in additional tax payable from clubs, players and agents.
“We take seriously allegations that customers or their agents may have acted dishonestly in the course of an enquiry, and can reopen closed cases if we suspect this has happened.”