Liberal senator Concetta Fierravanti-Wells questioned AUSTRAC officials about the matter at a Senate estimates hearing on Tuesday night.
"I can confirm AUSTRAC has looked into the matter and we've provided information to the AFP and to Victoria Police," Ms Rose told the hearing.
Ms Rose did not go into the nature of the information or why it had been passed on to the state and federal police.
SBS News had sought comment from both the AFP and Victoria Police about whether active investigations are ongoing.
In a statement, a spokesperson for the AFP confirmed it was undertaking a review of the "relevant information".
"The AFP has concurrently referred aspects of this matter to the Victorian Independent Broad-based Anti-corruption Commission (IBAC)," the spokesperson said.
"The AFP has no further comment to make on this matter."
Italian media did not provide any evidence to support the claims.
Senator Fierravanti-Wells also asked Home Affairs boss Mike Pezzullo if his department had received any requests from Cardinal Pell's legal team to examine the matter.
Mr Pezzullo said he wasn't aware of anything being received but would look into it.
A full bench of the High Court of Australia unanimously decided to quash the conviction of Cardinal Pell earlier this year.
Cardinal Becciu's lawyer has reportedly said his client strongly denies any interference with Cardinal Pell's trial.
Cardinal Becciu resigned his high-ranking post within the Vatican in September, reportedly after he was told to resign by Pope Francis.
Cardinal Pell then issued a statement praising Pope Francis and saying he hoped "the cleaning of the stables continues in both the Vatican and Victoria".
This appeared to reference allegations his prosecution in Victoria was in some way connected to his efforts to root out corruption and waste in the Vatican.
Viv Waller, a lawyer for a man who gave evidence against Cardinal Pell in the 2018 trial, has denied her client received any money.
Cardinal Pell's barrister, Robert Richter QC, has previously called for an investigation into reports about transfers from the Vatican.
"I am treating these reports as requiring a proper investigation by all fiscal authorities to track the money coming to Australia," he said earlier this month.
Cardinal Pell returned to Rome this month.