Tories in the city are calling on the Labour-run authority to raise the flag outside the Civic Centre to commemorate 'Brexit Day' on January 31.
The plan, which is set to be discussed at a full council meeting on January 29, has been branded a "political stunt" by Labour councillors in the city who have urged the Tories to concentrate on "bread and butter issues".
It comes after a national campaign was launched to make Big Ben chime on the hour Britain leaves the EU.
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Conservative councillor Simon Bennett, who put forward the motion, said: "Whether you voted leave or remain in the EU referendum, it is right that we mark this historic occasion of the UK formally leaving the European Union.
"Now is the time to come together as our country begins a new chapter, and I can think of no better way to unite the city than to fly the Union Flag on January 31.
"Now that we are finally getting Brexit done, with the support of a majority of Wolverhampton residents, the Government and indeed Wolverhampton Council itself can move on and start to work on the many challenges facing our city.
"I hope that councillors from across the political divide will support my motion."
Bilston East Labour councillor Stephen Simkins said he had "no problem" with flying the flag, but said there were far more important issues to deal with in the city.
"If that's what floats the Tories boat then carry on, I'll support it," he said.
"But I've got two pockets full of problems that I want to see dealt with.
"What about youth unemployment, the pressure the hospital is under, the fact that my town centre is dying away and the state of the roads?
"Is flying a flag going to resolve some of those issues?"
Councillor Milkinder Jaspal, for Heath Town, said: "This is a complete waste of time. The Conservatives need to get real and concentrate on the bread and butter issues of local government rather than this political stunt."
Labour councillor Phil Page, who represents Bilston North, said: "I'm proud to be English and have no issue with flying the flag.
"My only problem is when individuals try and make political capital out of using the flag. I'm sure Councillor Bennett would never do that."
The city council says it flies a number of different flags at the Civic Centre throughout the year in support of local, national and international campaigns and events.
In January 2019 a Tory plan to fly the Black Country flag in the city on a permanent basis was rejected.