The Regimental Blues, who have been at the centre of several high-profile controversies in their short life, will march on the morning of March 16 instead of the afternoon, when Aberdeen and Inverness supporters will flock to Celtic Park.
The group had originally proposed to march from the vicinity of Celtic Park in the east end of the city to George Square and back at midday and ending near 3pm in the Bridgeton area.
The council has had the parade moved to a 9.30am start to avoid clashing with the Aberdeen and Inverness fans heading to Celtic Park or arriving at Queen Street station.
Around 100 people are scheduled to take part in the parade by the group, which describes itself as a "pressure Group standing for the Protestant Loyalist Community of Scotland".
The Regimental Blues have had parades moved in the recent past.
Last September it was ordered to re-route an event and change the date after organisers said they wanted to march through a section of Glasgow's east end "to put a burning stick into the nest".
They were told by Police Scotland and Glasgow City Council the march posed a threat to public order, falling on a weekend with several major football games in the city, the Liberal Democrat conference and Bedroom Tax protests, as well as intelligence of counter-demonstrations.
In January, on the back of its opposition to a Bloody Sunday parade, it's online petition was reported to Police Scotland after the city council claimed comments made about a senior authority official were abusive and threatening.
And last month, Regimental Blues chairman Kris McGurk, who describes himself as a former British soldier, confronted the head teacher of a Glasgow secondary because the school is leased after hours by a council arms-length body to an Irish Republican band, as well as other groups.
Threats to picket the school led to a long-standing music school attended by hundreds of children being cancelled.
A city council spokesman said: "The organisers originally informed us of their intention to carry out two processions on the Sunday afternoon, which would have created a significant clash with the arrival of spectators heading to the League Cup Final.
"Officers have negotiated with the organisers and police to agree a much earlier start time, which will see the processions take place in the morning and minimise any conflict with football traffic."
A Police Scotland spokesman said police were "well-versed" in policing large events.
They said: "Each of these events will be policed appropriately."