Justice Secretary Humza Yousaf said today that the marches are a "stain on the city's reputation" after a second weekend of violence which saw a policeman injured by a firework during clashes.
Labour's James Kelly asked whether consideration has been given to "consolidating" the number of marches staged by particular organisations.
This would mean "if one organisation has a number of applications over a calendar period they're merged into one or a (smaller) number of marches in order to reduce number of marches taking place and therefore minimise disruption to local areas."
Mr Yousaf said: "I think we should look at all these proposals.
"I can give James Kelly an absolute assurance that this was part of the discussion we had with Glasgow City Council. Can they rationalise the number marches and therefore reduce the number of marches taking place?
"The challenge of this is that each of the applications often come in from different organisations.
"So the Apprentice Boys of Derry would be a very different organisation to the main Orange Order march that takes place around the 12th of July, although they may well be grouped under the umbrella of Loyalist parades."
The Government is looking at whether "mediation" among all the groups concerned could help reduce the number of marches.
Mr Yousaf praised the efforts of the police to contain trouble at two republican marches in Glasgow last weekend, which were met by counter demonstrations, and wished the officer injured by a firework a speedy recovery. It followed pitched battles in the streets of Govan the previous weekend after another Republican march was marred by clashes with protesters.
"The events of the last weekend have really demonstrated that sectarian violence is not a thing of the past," Mr Yousaf added..
"What we have seen is the perfectly legal right to parade peacefully and counter demonstrate, which are both important parts of a democracy which values free speech, being abused by those who are intent on denying others a voice so they can indulge in violent and disorderly behaviour.
"The right to free expression does not give you the right to intimidate communities.
"I can safely say that the vast majority of citizens in Glasgow view the sectarian violence stemming from these marches as a stain on the city's reputation."
The Scottish Government has been working with Glasgow City Council and Police Scotland to resolve the matter, including the prospect of fresh legislation. Council leader Susan Aitken has also pledged to tighten procedures in the way it allows marches to happen.