Despite being stripped of his title last year, the former prince remains eighth in line to the throne, and an Act of Parliament would be required to remove him entirely.
Parliament last removed a member of the royal family from the line of succession during the abdication crisis of 1936.
Any changes to the line of succession would require the agreement of the 14 Commonwealth countries which share the King as head of state, including Australia, Canada and Jamaica.
Albanese, an avowed republican, had recently announced he had no intention of holding a referendum on making the country a republic.
Albanese said he would not revisit the issue after meeting the King at Balmoral Castle in September last year. At the time, he said his government had more pressing concerns to address, such as the cost-of-living crisis, rather than ditching the King as their head of state.
Elsewhere, nine other police forces are assessing claims relating to Epstein and Mountbatten-Windsor.
Over the weekend, Britain’s Defence Minister Luke Pollard became the first senior minister to back calls for Mountbatten-Windsor’s removal from the line of succession, saying it was “the right thing to do” when he was “only a heartbeat away” from the throne as eighth in line.
Pollard told BBC Radio 4’s Any Questions programme that he hoped the proposals would “enjoy cross-party support”, but that “it was right that it is something that only happens when the police investigation concludes”.
Following his brother’s arrest, the King said that “the law must take its course”.
In a message signed “Charles R”, he wrote: “I have learnt with the deepest concern the news about Andrew Mountbatten-Windsor and suspicion of misconduct in public office.
“What now follows is the full, fair and proper process by which this issue is investigated in the appropriate manner and by the appropriate authorities.
“In this, as I have said before, they have our full and wholehearted support and co-operation. Let me state clearly: the law must take its course.”
Police are continuing to search Mountbatten-Windsor’s former home, Royal Lodge, in Windsor, Berkshire, following his arrest. He has denied any wrongdoing regarding his links to Epstein.
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