The government is considering introducing legislation to remove Andrew Mountbatten-Windsor from the line of royal succession, the BBC understands.
The move, which would prevent Mountbatten-Windsor from ever becoming King, would come after the police investigation has concluded.
The King's brother remains eighth in line to the throne despite being stripped of his titles, including "prince", last October amid pressure over his ties to paedophile financier Jeffrey Epstein.
On Thursday,
Mountbatten-Windsor was released under investigation following his arrest on suspicion of misconduct in public office. He has consistently and strenuously denied any wrongdoing.
The government's proposal comes after some MPs, including the Liberal Democrats and SNP, signalled their support for such legislation.
Some Labour parliamentarians who have been critical of the monarchy told the BBC they were less convinced the move was required - in part because it is so unlikely the former Duke of York would ever get near to the throne.
In October, Downing Street said it had no plans to introduce a law to change the line of succession.
It would require an act of Parliament, approved by MPs and peers, and also need to be supported by all other Commonwealth countries that have King Charles as their head of state, as it would also affect their lines of succession.
The last time the line of succession was changed by an act of Parliament was in 2013, when the Succession to the Crown Act restored individuals who had previously been excluded because they had married a Catholic.
The last time someone was removed from the line of succession by an act of Parliament was in 1936, when the former Edward VIII and his descendants were removed due to his abdication.
Liberal Democrat leader Sir Ed Davey said police should be "allowed to get on with their job, acting without fear or favour".
He added: "But clearly this is an issue that Parliament is going to have to consider when the time is right, naturally the monarchy will want to make sure he can never become King."
The SNP would support removing Andrew from the line of succession if legislation is required, according to the party's Westminster leader Stephen Flynn.
https://www.bbc.co.uk/news/live/c70kjr9wjw0t
Labour MP Rachael Maskell, who represents York Central, has also backed the move.
She said: "I would support legislation to remove Andrew from the line of succession and to remove from the counsellor of state."
Counsellors of state can stand in for a monarch who is ill or overseas although, in practice, only working royals are expected to be called upon to fulfil those duties.
Mountbatten-Windsor stepped back from public duties in 2019 following a backlash after an interview with BBC Newsnight about his relationship with Epstein.
Conservative Party leader Kemi Badenoch said "all of us in public life need to give space" to the police investigation to be carried out.
Her remarks came after her Conservative colleague, shadow Scotland secretary Andrew Bowie, told GB News it "would be the decent thing" for Mountbatten-Windsor to remove himself from the line of succession.
Bowie said: "I think until the investigations have concluded, however, yes of course if he is found guilty of this, I think Parliament would be well within its rights to act and remove him from the line of succession."
The Conservative MP added Mountbatten-Windsor has "not been found guilty of anything just yet, he has yet to be charged with anything, so we have to let the police investigation run its course, and I think we should all act accordingly subsequent to that".
