The ruling Liberal Democrat group on York Council wants to revoke the city's highest honour which was granted to the Prince in 1987.
The City of York Council was due to hold an extraordinary meeting on Thursday evening to consider the motion: "The Council resolves that pursuant to Section 249 of the Local Government Act 1972, the City of York Council withdraws the Honorary Freeman of the City status from the Duke of York which was conferred upon him in 1987."
It comes after his out of court settlement of a civil sex assault case in the US brought against him by Virginia Giuffre.
He's always maintained his innocence.
The Lib Dems and the city's Labour MP also want him to lose his title of Duke of York.
Buckingham Palace declined to comment on the matter when approached by ITV News.
Lib Dem councillor Darryl Smalley said: "When you look at international and national coverage of the saga he's constantly referred to as the Duke of York - that intrinsically links our city to him and the allegations against him.
"I think it's right that we as councillors do what we can to show it's an association we no longer think is appropriate."
Rachael Mascall, the Labour MP for York Central, said: "As a centre for tourism, of course, people come to York and enjoy the city but it's the right reputation that we want to protect.
"What I have done is I have written to Prince Andrew and asked whether or not he would relinquish his title or not - I await his reply."
It was proposed that the meeting could be held online but opposition councillors called for it to be postponed until it could be held in person.
The council say that the meeting will take place later in April.
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