As commemorative processions get under way in Glasgow today, the Grand Orange Lodge of Scotland has urged its members to make their voices heard before the survey ends on July 11.
Glasgow City Council introduced its policy on parades four years ago and the latest review could see restrictions changed if councillors rubber stamp the plans at an executive committee meeting next month.
The council has written to groups about the consultation but a source revealed "only a handful of stakeholders have responded".
The new policy could include changes to the time of parades and the playing of drums as well as a revised definition of a place of worship.
Robert McLean, executive officer at the Grand Orange Lodge of Scotland, said: "It's not perfect - but as far as we're concerned it's an improvement."
Mr McLean was part of a group chaired by Councillor Philip Braat, who has revealed that he will oversee today's parade.
Mr Braat has been tasked with steering the review through the executive committee. He said: "A big part of the task has been working closely with organisations that hold processions to almost professionalise their approach to event planning.
"They need to know what we expect of them and, in turn, we need to be clear about what we will and won't support.
"The current proposals are about fine-tuning our policy."
The council's figures show a 21.5% reduction in the number of all parades over the past five years, from 497 in 2009/10 to 390 in 2013/14.
Tomorrow's Orange Order procession will see around 6000 people march through Glasgow, with another 1000 expected to join a rally at Glasgow Green.
Driving restrictions will be in place on 31 streets between 9.30am and 4pm, including Gallowgate, Trongate, High Street, Ingram Street and roads bordering George Square.