The government is considering introducing legislation to remove Andrew Mountbatten-Windsor from the line of royal succession,
BBC reports.
Defence Minister Luke Pollard told the BBC the move - which would prevent Andrew from ever becoming King - was the "right thing to do," regardless of the outcome of the police investigation.
Currently Andrew, 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 evening, Andrew was released under investigation 11 hours after his arrest on suspicion of misconduct in public office. He has consistently and strenuously denied any wrongdoing.
Speaking on BBC Radio 4's Any Questions programme, Pollard confirmed the government had "absolutely" been working with Buckingham Palace on the plans to stop the former prince from "potentially being a heartbeat away from the throne".
He said this was "something that I hope will enjoy cross party support, but its right that that is something that only happens when the police investigation concludes".
Chief Secretary to the Treasury James Murray told the BBC that "any questions in that sphere would be quite complicated", adding that the live police investigation needs to "play out".
On Saturday, several unmarked police cars were again seen entering Royal Lodge, the 30-room Windsor property where Andrew lived for many years.
At one point on Friday more than 20 vehicles could be seen parked at the property, although it is not known it all was connected to the investigation and searches.
Thames Valley Police, the force which arrested him, is expected to continue searching Royal Lodge until Monday, the BBC understands.
Several other forces across the UK are also considering whether to launch investigations, noted Danny Shaw, a former adviser to ex-home secretary Yvette Cooper.
"It has the danger of spiralling out of control," Shaw told Radio 4's Today programme. Because of this, these investigations could take "considerable time", he added.
The government's proposal to remove Andrew from the line of succession 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.
After the latest revelations, historian David Olusoga told BBC Newsnight there is now "a desperate desire within government and within the palace to draw a firewall… between this crisis and the wider monarchy".
Buckingham Palace has not publicly commented on the government's plans to remove Andrew from the line of succession.
