Bishop Ingham, 73, said he was unlikely to be chosen as archbishop because of his age.

"They would be looking for a younger and more long-term archbishop," he said.

"I would consider others would have more credentials.

"If I was chosen I would have to really consider it, but I doubt that I will be."

The Bishop congratulated Cardinal Pell on his role as "budget supremo" aimed at overhauling the Church's bureaucracy to better help the poor and disadvantaged.

"I wish him well in a difficult job," he said.

"I know he will bring to it a great wealth of experience and knowledge."

Bishop Ingham said he did not have inside knowledge of who would replace Cardinal Pell but would be praying for a worthy successor.

Pope Francis revealed Cardinal Pell's appointment on Monday, making him one of the most powerful men in the Church.

As Prefect for the Economy of the Holy See, he will work in a new body with authority over the Holy See and Vatican's economic and administrative activities.

He will oversee the finances of the Holy See and the Vatican City State, which includes the profit-making Vatican Museums and Vatican's post office. The shake-up follows a wave of scandals at the Vatican bank and is the first major overhaul of its bureaucracy in 25 years.

Cardinal Pell said the new system would implement changes to management, improve financial planning, reporting and auditing and involve more senior lay experts in policy making.

Cardinal Pell said he was deeply honoured to have been chosen for the role.

"If we make better use of the resources entrusted to us we can improve our capacity to support the good works of the Church, particularly our works for the poor and disadvantaged."

Cardinal Pell said the church needed to be open to opportunities to improve its financial administration.