Flying the Union flag from the cenotaph at Belfast City Hall would be a reasonable compromise, the Alliance Party has said.
Maire Hendron, whose party holds the balance of power on Belfast City Council, said she was likely to back the proposal when it comes before a committee meeting in the New Year.
Mrs Hendron said: "It is a reasonable proposition and I am not ruling it out. I probably would when the time comes following discussion with our party."
On Monday night, city councillors voted 29 to 21 in favour of changing their policy and have the Union flag flown from the main building on 17 designated days.
The decision sparked scenes of violence where 18 people including 15 police officers were injured. Missiles such as bricks and fireworks were thrown at police lines and Irish tricolours were burnt.
The proposal to fly the flag 365-days a year from the cenotaph in the Garden of Remembrance at the west side of City Hall was put forward by the DUP's Lee Reynolds. It would require support from the Alliance Party to be passed.
Speaking on Radio Ulster Mrs Hendron said: "It was something that had been mentioned to me some days ago by a member of our party in another area. It was something I was prepared to discuss with my party and my group. But, last night was not the place and not the time to discuss it."
Mrs Hendron said the move may not be enough to assuage the anger of loyalists, adding: "They have been whipped up."
Meanwhile, Sinn Fein councillor Jim McVeigh said his party would oppose flying the Union flag from the cenotaph and described revisiting the controversial issue as madness.
He said: "It would be crazy for anyone to support such a suggestion. It would be a huge mistake to repeat the same thing again in a few weeks time."