An act of parliament would be required to remove him.
Keir Starmer's government will consider introducing such legislation once the police have finished their investigation into him, the Press Association understands.
Any changes to the line of succession would also require the agreement of other countries, including Australia, that share the UK monarch.
Meanwhile, UK Detectives have urged the former prince's past close protection officers to "consider carefully whether anything they saw or heard" is relevant to their investigation into paedophile financier Jeffrey Epstein and his associates.
The Metropolitan Police said it was also working with counterparts in the US to establish whether London airports had been used to "facilitate human trafficking and sexual exploitation".
On Friday, the force said no new reports of alleged sexual offences have been made since the release of millions of pages of documents related to Epstein by the US Department of Justice.
It follows Andrew's arrest on Thursday on suspicion of misconduct in public office, which saw him held in custody for 11 hours before being released under investigation.
The force previously said it was looking into allegations Andrew's protection officers turned a "blind eye" to his visits to Epstein's island, Little St James.
Police are yet to identify any wrongdoing by close protection officers.
Andrew's primary accuser, Virginia Giuffre, alleged she had sex with him during an orgy with "underage" girls on the Caribbean island.
The former prince has previously vehemently denied all allegations made against him.
"The Met is identifying and contacting former and serving officers who may have worked closely, in a protection capacity, with Andrew Mountbatten-Windsor," police said.
"They have been asked to consider carefully whether anything they saw or heard during that period of service may be relevant to our ongoing reviews and to share any information that could assist us."
Police urged anyone with new or relevant information to come forward.
"All allegations will be taken seriously and, as with any matter, any information received will be assessed and investigated where appropriate," the statement said.
Searches have been ongoing at Andrew's former home - Royal Lodge, in Windsor, Berkshire - following his arrest on suspicion of misconduct in public office on Thursday.
He became the first senior royal in modern history to be arrested after being taken into custody on his 66th birthday.
Thames Valley Police, who are leading that investigation, are yet to receive any "early investigative advice" from the Crown Prosecution Service in relation to the allegation, it is understood.
The arrest came after Andrew was alleged to have shared sensitive information with Epstein during his time as the UK's trade envoy.
On Friday, a helicopter circled Royal Lodge, with unmarked vans, believed to be police vehicles, entering the grounds throughout the morning.
A police presence remained at the Sandringham Estate but searches of Andrew's Norfolk home concluded on Thursday.
The arrest of the King's younger brother made headlines across the world, including a picture of him looking drained and exhausted, slouched in the back of a vehicle leaving Aylsham police station.
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