A law to remove Andrew Mountbatten-Windsor from the line of succession will be considered by the UK government after police finish investigating the king's brother, it is understood.
An act of parliament would be required to remove him.
Prime Minister Keir Starmer's government will consider introducing such legislation once the police have finished their investigation into him, it is understood.
Any changes to the line of succession would also require the agreement of other countries which share the UK monarch.
It comes after Mr Mountbatten-Windsor's arrest yesterday on suspicion of misconduct in public office. He was held in custody for 11 hours before being released under investigation.
Detectives continued to search Mr Mountbatten-Windsor's former home in Berkshire today.
He was held yesterday morning after allegations were made against him following the release of files related to paedophile financier Jeffrey Epstein.
Mr Mountbatten-Windsor has denied any wrongdoing over his Epstein links, but has not directly responded to the latest allegations.
After his arrest, King Charles said in a statement that "the law must take its course" and the police have "our full and wholehearted support and co-operation".
Searches at a property in Norfolk - his home on the Sandringham Estate - have concluded, however, Thames Valley Police said the searches they were carrying out a Berkshire address - his former home of Royal Lodge on the Windsor estate - would continue.
Mr Mountbatten-Windsor was pictured slouching and looking drained and exhausted in the back of a vehicle as he left Aylsham police station in Norfolk yesterday evening.
He arrived back at Sandringham later, his car sweeping past waiting journalists.
Yesterday evening, US President Donald Trump said the arrest was "very sad". The US President added: "I think it's so bad for the royal family."
Mr Trump, speaking to reporters as he headed to Georgia for an event, praised King Charles, and said he "would be coming to our country very soon".
He said: "When I see that, it's a very sad thing. To see it, and to see what's going on with his brother, who's obviously coming to our country very soon, and he's a fantastic man, the king, so I think it's a very sad thing."
The former duke was detained on his 66th birthday over allegations he shared sensitive information with Epstein while serving as the UK's trade envoy.
Thames Valley Police previously said the force was reviewing allegations after emails released by the US Department of Justice appeared to show Mr Mountbatten-Windsor sharing reports of official visits to Hong Kong, Vietnam and Singapore with the disgraced financier.
One email from the files, dated November 2010, appeared to be forwarded by Mr Mountbatten-Windsor five minutes after being sent by his then-special adviser Amir Patel.
Another, on Christmas Eve 2010, appeared to show he sent Epstein a confidential brief on investment opportunities in the reconstruction of Helmand province in Afghanistan.
Mr Mountbatten-Windsor has denied any wrongdoing over his Epstein links, but has not directly responded to the latest allegations.
Watch: Andrew Mountbatten-Windsor leaves police custody
It is understood that neither King Charles nor Buckingham Palace had been informed before the arrest yesterday morning.
However, the British Home Secretary was alerted to the arrest shortly before Mr Mountbatten-Windsor was taken into custody, it is understood.
Thames Valley Police denied briefing the Home Office before the arrest, but issued a statement from the National Police Chiefs' Council to clarify that the NPCC did so.
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The statement read: "In line with routine practice, the National Police Chiefs' Council alerted operational colleagues within the Home Office of the arrest. This gave 30 minutes' notice before Thames Valley Police made the arrest."
At around midday, Charles released a statement in which he said the police "have our full and wholehearted support and co-operation".
"Let me state clearly: the law must take its course," he added.
Charles carried on with his duties after Mr Mountbatten-Windsor's arrest with planned ambassadorial in-person audiences in the Throne Room at St James's Palace.
While arriving at an engagement in The Strand, central London, Charles was met with questions about his brother which he did not respond to.
Mr Mountbatten-Windsor became the UK's special representative for international trade and investment in 2001.
He stepped down in 2011 amid the furore over his friendship with Epstein.
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