It is claimed that the duo could have hidden 150 million euros in tax havens in Switzerland and the British Virgin Islands.
A group of 12 European newspapers said it intends to disclose over the next three weeks the results of investigations into widespread alleged corruption at the heart of football under the banner "Football Leaks".
Both Ronaldo and Mourinho say that they have fully complied with British and Spanish fiscal requirements.
Based on leaked documents obtained by German weekly Der Spiegel, the outlets claim that Real Madrid and Portuguese star Ronaldo could have "hidden 150 million euros in tax havens in Switzerland and the British Virgin Islands".
"On this amount, the striker paid only 5.6 million euros in taxes, or barely four percent," added the report.
Ronaldo, it is claimed, benefits from "a system developed by his agent Jorge Mendes".
They cite two operations related to advertising revenue of the Portuguese star.
The first, between 2009 and 2014, could represent "74.8 million euros via an offshore company called Tollin, registered in the British Virgin Islands", said the report released Friday.
"He would have eventually declared a part of it," added the report sent to AFP by the Mediapart organisation.
"The lawyers of the player told the (media) consortium that a Spanish tax audit aimed at Cristiano Ronaldo was still in progress," the newspapers said.
In the second operation, Ronaldo could have "avoided 31 million euros of taxes" according to these newspapers, making the most of "12 days of an ultra-advantageous tax regime" on his marketing rights for the period 2015-2020.
According to the European Investigative Collaborations (EIC) consortium, Manchester United manager Mourinho is said -- again via Mendes -- to have "concealed 12 million euros in a Swiss account owned by a British Virgin Islands company".
It was "subject to a tax audit in Spain... which resulted in a recovery of 4.4 million euros, penalties included".
Friday's first batch of leaks centred on "a system" put in place, according to the newspapers, by Mendes, the super-agent of Ronaldo and Mourinho.
The system overall would have accounted for a loss of "at least 185 million euros of sponsorship income from the tax administrations through a network of offshore accounts and offshore companies in Ireland, the British Virgin Islands, Panama and Switzerland".
In response, Mendes's company Gestifute said Friday that Ronaldo and Mourinho had "fully respected their obligations vis-a-vis the Spanish and British authorities".
The company accused the media consortium of operating in an "insidious" way concerning the stars' tax obligations.
It said that neither Ronaldo nor Mourinho "have been implicated in legal proceedings of the tax evasion commission in Spain".
Earlier Friday, Gestifute said that last March "a number of societies linked to the world of football were the victims of cyber-attacks" which saw the leaking of documents published by Football Leaks "in several countries in Europe, notably Spain".
The company noted they had taken legal redress against claims of tax evasion and stressed it had always acted with "the highest degree of professionalism in relations with (its) clients and authorities".
More than 18 million leaked documents have been examined in the expose.
In weeks to come, the media organisations, which include Der Spiegel, The Sunday Times in Britain and Spain's El Mundo, say they will also publish allegations of prostitution and exploitation of minors in football.