Police are investigating a potential breach of Italy's COVID-19 regulations by Juventus forward Cristiano Ronaldo after he allegedly travelled between the regions of Piedmont and Valle d'Aosta.

Valle d'Aosta police confirmed to Reuters that an investigation has been opened into a trip to the Alpine town of Courmayeur by Ronaldo and his girlfriend Georgina Rodriguez on Tuesday and Wednesday.

Authorities were alerted to his alleged presence in the region by videos on social media showing the couple sitting on a snowmobile and celebrating Rodriguez's 27th birthday.

Movement between 'orange zone' regions in Italy, including Piedmont and Valle d'Aosta, is forbidden under the current government decree.

If Ronaldo is proven to have made the trip, the likeliest outcome is a fine. ESPN has approached Ronaldo's representatives for comment.

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In October, Ronaldo became involved in a public row with Italy's sports minister as the pair indirectly accused each other of lying over whether the Portugal international had broken health rules after testing positive for the coronavirus.

Vincenzo Spadafora said the Juventus forward might have infringed the rules by flying back to Italy from national team duty in Portugal after he tested positive for the virus earlier this week.

But in an Instagram video, Ronaldo hit back and said he had done everything by the book.

"A gentleman here in Italy, whose name I won't mention, said I didn't obey the protocol -- that's simply a lie," said Ronaldo from his Turin villa, where he was in quarantine and asymptomatic.

"I followed all the protocols and I will continue to follow them, my conscience is clear.... Everything I did was authorised."

The 35-year-old tested positive for COVID-19 while he was with the Portugal squad.

"They said I broke Italian law and this and that... it's all lies, I did everything properly," he added. "We did everything the right way -- leaving the [Portugal] team, in the air ambulance, arriving in Turin... I did not have contact with anyone."

Spadafora later replied in an interview with the Italian news agency Ansa.

"The fame and skill of certain players does not entitle them to be arrogant, disrespectful to the institutions and to lie," he said.

"On the contrary, the more well known you are, the more you should feel the responsibility of thinking before speaking and setting a good example.

"I'm not going to continue with this matter forever," he added. "I'm not talking about it again and I repeat my wish that everyone who has tested positive recovers quickly."