The Alliance Party has written to the UK government asking it to remove Prince Andrew's birthday from its formal list of designated days for flying the Union flag.
It is seeking agreement with other parties that the flag is not flown from Belfast City Hall on February 19 and for an alternative date to be chosen.
The move follows calls to drop the Duke of York's birthday from the UK list of designated days as the Royal faces civil action in the US over sexual assault allegations.
Belfast City Hall has flown the Union flag on designated says since a vote in December 2012 to end its permanent display.
The decision sparked weeks of street protests and disruption as loyalists clashed with police.
Guidance on designated days for flying the Union Flag from government buildings is determined by the Department for Digital, Culture, Media & Sport (DCMS).
Alliance councillor Nuala McAllister, the party's group leader on Belfast City Council, said the guidance on designated days should be changed on a UK-wide basis.
She told Belfast Live: "We've already written a letter to DCMS, the department in Westminster, to ask them that they remove Prince Andrew's birthday from the list of designated days.
"And one thing that we have also suggested is that another day is added on to designated days.
"Because that's a compromise position, and everyone knows that flags is a sensitive issue in Belfast and Belfast City Council."
If DCMS does not change its guidance on the Union flag, she said: "We will engage with other parties here to agree that it's not flown on his birthday but actually that another date at another time it is flown.
"And one example that we have given in the past is to mark the Somme here in Belfast."
Ms McAllister added: "We need to make sure that everything that people and public representatives do in particular is to support victims in coming forward by saying just because of who that person is doesn't mean that they will be protected at all costs."
The Duke of York is being sued in the US by Virginia Giuffre, who claims he abused her in 2001 when she was 17. Prince Andrew denies the allegations.
SDLP has also called for Belfast City Hall not to fly the Union flag on Prince Andrew's birthday.
Independent unionist councillor John Kyle told The Irish News he would support the flag not being flown on February 19.
DUP deputy lord mayor Tom Haire said the date should remain a designated day "until the government directs otherwise".
Ulster Unionist councillor Jim Rodgers said the matter should be examined because of the allegations, but it was "only right and proper that you are considered innocent until proven guilty".
