Glasgow City Council is looking at new guidelines to ensure pet owners keep their dogs under control and close at heel and could also block people from walking more than three animals at a time.
In a new Parks Management Rules document that has been put out for public consultation, officials have proposed that dogs are kept on a lead no longer than six feet when in city parks, and are prevented from creating a nuisance to other park users.
However, the council insists this would not prevent people from playing fetch with their pets or letting dogs off the leash as long as they are still in control of the animal.
The guidelines, if given the go-ahead, will affect the local authority's 600,000 residents.
The Dogs Trust, which has a centre in Glasgow, said it was hoped any new rules would be not prevent dogs from being properly exercised.
A spokeswoman for the charity said: "I know there have been negative reports about dogs lately, but the majority of dog owners in Scotland are responsible and are able to keep their dog under control. We would argue that letting a dog off the lead is fundamental to its welfare. Dogs have to be able to exercise - they have to be able to interact with other dogs.
"They have to be able to run off the lead, and if they're not allowed to, that is absolutely detrimental to a dog's health and wellbeing."
She added: "It will particularly affect people who don't have a garden, or have a small garden, who maybe don't have the means to get out of the city and who let their dogs off to run around the local park."
However, some dog owners reacted with horror to any changes to the rules.
Steven Campbell, 29, from Glasgow city centre who has an 18-month Cockapoo, called Fudge, said: "It's a terrible idea. If a dog is aggressive or unsociable then fair enough.
"However, this could lead to further issues as a dog that can't release its energy in the park or off lead will be more likely to suffer with behavioural problems.
"It would make more sense to have smaller dog park areas within the grounds where you can exercise your dog and socialise them properly."
Another owner, who asked not to be named, said: "Dogs need to be able to belt about to let off steam. My five-year-old mongrel Lassie is a damned sight more sociable off the lead than on it. If a dog is aggressive and dangerous, that is an entirely different matter - it should be muzzled or put down."
A council spokesman said: "The park management rules are reviewed every 10 years.
"The main aim of this consultation is to simplify the rules and make it easier for visitors and the people of Glasgow to enjoy the city's parks.
"We want to ensure that people can enjoy the parks without being caused any nuisance and that park users behave in a safe and responsible manner.
"It is hoped that all interested parties will make their views known by taking part in the consultation."