Reports in Spain say Ronaldo is suspected of defrauding €15m (£13m, $17m) between 2001 and 2014 linked to money earned from the use of his image.
Leaked documents have suggested that the Portuguese footballer avoided tax on income from image rights allegedly held in offshore accounts.
Ronaldo has denied the claims.
However, if he does head to court, the two-time winner of Fifa’s Balloon d’Or for world player of the year could face tougher sanctions than Messi having reportedly avoided paying tax on more than three times the sum his rival has been convicted of stashing offshore.
Argentinian footballer Messi and his father Jorge were convicted of defrauding Spain of €4.1m in taxes in July 2016. Their appeal was denied on Wednesday, when Spain’s Supreme Court upheld the verdict.
The Barcelona player and his father were found guilty of three counts of tax fraud, however neither is likely to spend any time behind bars as, under Spanish law, prison sentences of less than two years can be served under probation.
In addition to the jail terms, Lionel Messi was fined around €2m and his father €1.5m for using tax havens in Belize and Uruguay to conceal earnings from image rights.
Both also made a voluntary ‘correction payment’ of €5m in August 2013, which equated to the value of the unpaid tax plus interest.