The Australian cardinal who oversees the Vatican's finances has strongly denied newspaper allegations of involvement in child sexual abuse, describing them as "utterly false".

The Sun Herald newspaper reported late Friday that Cardinal George Pell was being investigated by Australian police over allegations of abuse while he was serving in senior positions within the Catholic Church in Australia.

Pell has called for a public inquiry to be conducted into police in the state of Victoria, saying the allegations were leaked "to do maximum damage" before he gives evidence at the end of the month to a child abuse inquiry in his homeland.

Victorian police said they could not comment on any investigations into any individuals.

Pell, once seen as a contender to become pope, was cleared earlier this week to testify at the Royal Commission into Institutional Responses to Child Sexual Abuse via videolink, because of a heart condition.

The ruling frustrated victim groups who wanted him to appear in person. They have since begun a crowdsourcing campaign to raise money to travel to Rome in the hope of seeing him testify in person.

The Sun Herald report said Victorian police had compiled a dossier containing allegations that Pell committed "multiple offences" when he was a priest in Ballarat, a town in the west of the state, and also when he was archbishop of Melbourne. The inquiry has been gathering evidence for a year, the paper said.

In a lengthy statement issued by his office in Rome in response to the report, Pell called on senior police and government officials to "immediately investigate the leaking of these baseless allegations."

"The allegations are without foundation and utterly false," the statement said. "These undetailed allegations have not been raised with the Cardinal by the police."

Pell would cooperate with police if they wished to question him, the statement added.

The Royal Commission heard testimony last year that priests suspected of abuse in Pell's former diocese were moved between parishes and put in church-appointed rehabilitation instead of being reported to police.

Pell, 74, has denied those allegations. He is due to testify from Rome via videolink on February 29.