An impromptu demonstration is due to take place in George Square at midday on Saturday as loyalists protest against the decision to limit the number of days the Union flag is flown at Belfast City Hall.
At the same time, a commemoration march is being organised by republican group Cairde na hÉireann and is scheduled to leave from the city's Cowcaddens area at noon and travel around the centre.
Anti-sectarian campaigners have called for both groups to ensure their protest is a peaceful one, while Strathclyde Police confirmed they will police both events appropriately.
The flag decision in Belfast has already resulted in violence in the Northern Irish city, including the attempted murder of a police officer whose patrol car was petrol bombed.
Nil By Mouth campaign director Dave Scott said: "The events of the last week show the hold flags and emblems still have over us, even in this era of globalisation.
"Scotland is not immune from this and people on all sides of this debate will hold strong views. We have always supported the right to demonstrate but we urge those involved to make their point in a peaceful, dignified fashion. Anything else is unacceptable.
"Many retailers are relying on a good Christmas to keep people in jobs and I would hope people will be able to go about their business uninterrupted."
The George Square protest – which will also clash with a children's winter wonderland fair – is being organised by different Facebook groups, which are being monitored by police.
One social network page read: "In support of our fellow British citizens in Northern Ireland, can all proud Scottish/British patriots descend on the City's George Square at 12pm on Saturday, December 15, for a mass protest. No Surrender."
The republican march is the Volunteer Sean McIlvenna Commemoration Parade and is expected to attract around 350 participants. It will leave Shamrock Street at 12pm, passing along Cowcaddens Road and on to North Hanover Street which adjoins George Square.
A spokesman for Glasgow City Council confirmed the republican march is going ahead on Saturday, but said the council had not been officially notified of any demonstration taking place in George Square.
A spokeswoman for Strathclyde Police said: "Demonstrations will be policed appropriately to ensure any disruption to people in the city centre, especially at this very busy time, is kept to a minimum." She added that officers are aware of the Facebook site promoting the George Square demonstrations and are monitoring it.
A similar protest is also expected to take place in Kirkcaldy in Fife at 7pm on Sunday. Fife Council said they had no knowledge of the event but Fife Constabulary said they had been made aware of it.