According to allegations that have surfaced in the press, the Portuguese star has been invoicing for most of his advertising revenues through an Irish company, in which the name of the player does not even appear.
Spain's tax authorities disapprove of image rights going through a country other than the residence of the individual concerned.
It is claimed that since Ronaldo resides in Madrid, he should have paid taxes of 43.5 per cent of the advertising revenue generated to the Spanish tax authorities.
By not doing so, it is claimed the footballer has benefitted from a significantly lower tax rate on his earnings. While Spain taxes at 43.5 per cent, Ireland only charges 12.5 per cent.
Ronaldo is also accused of moving €63.5m to a tax haven in the Virgin Islands to avoid paying taxes.
There were also accusations that Jose Mourinho, the Manchester United manager, could also be involved in the same issue.
Mourinho is accused of moving €12m to a Swiss bank account operated by a company in the British Virgin Islands.
The allegations have appeared in the Spanish newspaper El Confidencial.
El Mundo, another Spanish newspaper, said the reason why the issue has been opened is because of Ronaldo's offshore activity in his 2014 tax declaration. The paper reported that Ronaldo earned almost €150m in advertisement copyrights but "in principle only paid €5.6m directly to Spanish tax authorities, less than four per cent of the total amount."
Ronaldo's management company, Gestifute, declared that the accusations were unfounded. They said in a statement that the player is in compliance with his fiscal obligations in Spain.
The allegations come amid calls from MEPs for a crackdown on tax avoidance.
The European Parliament set up a special committee to investigate the fallout from the Panama Papers scandal which highlighted how the rich and famous can avoid tax by using tax havens such as Panama and the Virgin Islands. The committee is due to conclude its work next year.
Reacting to the news, Giegold, a German deputy from Parliament's Greens/EFA group, told this website, "The tax dodging practices of football stars are a serious foul play against the common good.
"Tax avoidance by Ronaldo and other players is to the disadvantage of their fans and all other honest taxpayers. Not only on the playing field but also when it comes to paying taxes fair play should be the rule of thumb."
The MEP, who is currently campaigning against tax avoidance and evasion, added, "Once again it is Ireland that promotes tax dumping and takes away tax revenue from other EU countries.
"The tax tricks of football stars underline the need for curbing tax competition in Europe by introducing common minimum tax rates for companies."
He added, "The European Commission has to follow up with a legislative proposal."
It is not the first time football's top figures have been accused of tax evasion and financial irregularities. Lionel Messi was convicted of tax fraud this summer, but did not have to serve time in jail because it was a first offence.
Meanwhile, Messi's Barcelona teammate Neymar appears to be on track to stand trial over financial issues in his transfer from Santos to Barcelona.