Andrew was given the Honorary Freedom of the City of York in 1987 but Liberal Democrats, who form the largest group on City of York Council, said a motion to begin the process of removing the honour will be submitted at the next full council meeting on March 24.
The motion will also call for the prince to relinquish his title as Duke of York in the wake of the settlement of his legal battle with Virginia Giuffre.
Andrew had faced widespread calls for him to give up the dukedom, which is one of his last remaining major titles after the Queen stripped him of his honorary military roles and he gave up his HRH style.
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The honorary freedom of the city is bestowed to recognise notable service by local residents, to distinguished people, and to royalty, the council has said.
Other recipients of the honour include the Duke of Wellington, Sir Winston Churchill, film composer John Barry, and actress Dame Judi Dench.
Darryl Smalley, City of York Council’s executive member for culture, leisure and communities said: “Having been stripped of his military roles and royal patronages by the Queen, we are seeking to end Price Andrew’s links with our great city, including removing his Honorary Freedom.
“York’s unique connection to the Crown and the monarch is an important part of our city’s legacy and history.
“However, as a council and city, we stand with victims of sexual abuse and are doing all we can to end violence against woman and girls locally.
“As such, it is inappropriate that Prince Andrew retains his ambassadorial title that is intrinsically linked to our city.”
The Queen’s second son “regrets his association” with disgraced financier Jeffrey Epstein, a letter submitted to the United States District Court stated.
Andrew has agreed to make a “substantial donation” to Ms Giuffre’s charity after the pair agreed an undisclosed out-of-court settlement in her civil sex claim against him.
It has been reported he has agreed to pay an eight-figure sum.