Cardinal Pell, who returned to Rome on September 30, was freed after 18 months in jail when the High Court of Australia quashed his conviction in April.
Italian newspapershave reported that Cardinal Pell previously clashed with Cardinal Becciu when the Australian, as the Pope's finance minister, sought to expose alleged misappropriation of Vatican coffers.
La Repubblica and Corriere della Sera have quoted leaked documents that Vatican investigators suspected Cardinal Becciu of funnelling the money to Melbourne Supreme Court witnesses.
Investigators alleged Cardinal Becciu hoped the money would thwart Cardinal Pell's transparency program which would have exposed Cardinal Becciu's allegedly corrupt management of Vatican cash.
Cardinal Becciu has strongly denied the allegations, saying, "I categorically deny interfering in any way in the trial of Cardinal Pell."
As finance minister before returning to Australian in 2017 to face trial, Cardinal Pell had been assigned by Pope Francis to clean up Vatican accounting practices.
But Cardinal Pell's attempts were blocked by Cardinal Becciu, who had held an influential role in distributing and investing millions of euros of Catholic donations.
Cardinal Becciu had been deputy secretariat of state between 2011 and 2018 before Pope Francis removed him and placed him in charge of running the Holy See's department responsible for making saints.
Last month, the Pope sacked Cardinal Becciu from that job and stripped him of the right to elect popes.
This happened as Vatican investigators began to sift through Cardinal Becciu's secretariat of state spending record.
In question was a multi-million luxury property in Chelsea, London, which Cardinal Becciu oversaw and which allegedly lost the Vatican money while making millions for consultants.
In 2016, Cardinal Pell, whose right-hand man was Vatican's auditor-general, Libero Milone, ordered an audit of Vatican finances by an external accountancy firm.
Cardinal Becciu overruled the move, blocking the audit, and a year later engineered the ousting of Mr Milone, who was accused of spying on officials.
"Milone was Pell's right-hand man and the enmity between Pell and Becciu was huge," said Massimo Franco, author of a new book about Pope Francis, The Enigma of Bergoglio.
That enmity had been fuelled by a comment from Cardinal Pell which Cardinal Becciu felt amounted to his being called dishonest in front of the Pope.
Following Cardinal Becciu's sacking as secretariat, Pell had said: "The Holy Father was elected to clean up Vatican finances.
"He plays a long game and is to be thanked and congratulated on recent developments."
Cardinal Becciu protested, saying, "I couldn't allow him to say something like that.
"From the time I was a child, I had always been taught by my parents to be honest."
The war between the cardinals has dominated news of the Vatican as Pope Francis, in a document released on Sunday, urged the world to rediscover its sense of charity as it battled Covid-19.
The Pope said the coronavirus pandemic confirmed his belief that political and economic institutions must reform to address the legitimate needs of the people.