Thousands of runners took part in the annual event, through some of the city's best known streets, including Argyle Street and Byres Road, when it was at its peak in the early 1980s.
The 26.2mile race was launched in 1979 and continued to 1987, when numbers greatly declined. It was changed to a half marathon in 1988.
Lack of television coverage and the absence of a main sponsor were cited as possible reasons.
But hundreds of people have backed an online campaign on Facebook to re-instate a marathon in Scotland's largest city.
More than 23,000 took part in the Great Scottish Run – which combines a 10K and half-marathon – through Glasgow streets earlier this month. The number of participants was the highest so far.
Running enthusiasts believe it suggests there is an appetite for a full marathon.
A marathon will form part of the athletics programme at the Commonwealth Games in Glasgow in 2014.
The course is planned to start and finish at Hampden Park, but the route has not been finalised.
Glasgow Life, which organises the city's other running events, believes staging a full marathon would prove "challenging" due to the amount of road closures required and the cost.
But Jamie Yardley, 38, from Wishaw, Lanarkshire, who launched the campaign to bring back the marathon, said: "I launched the page (on Facebook) earlier this year and had forgotten about it.
"But since the Great Scottish Run I have been inundated with messages of support for a full marathon.
"I grew up in Glasgow and think it would be an amazing thing for the city.
"The Edinburgh Marathon contributes so much to the city."
One runner who backed the campaign said: "Glasgow is a large city. If Edinburgh, London and Inverness can organise a suitable route staying away from main dual carriageways, why can't Glasgow?
"They hold other road races well so I am sure the demand is there. I know I would certainly run it."
Tammy Ward, a coach with Glasgow Running Network, said: "On the back of the success of the Olympics Games and the Great Scottish Run festivities, it would be fantastic to see Glasgow using its position as a top tourist destination and beautiful location to host a marathon.
"It seems a natural progression for a city that holds a range of top class running events throughout the calendar.
"The Glasgow Running Network would be able to offer suitable training programmes to support training.
"I would certainly take part and think in the run-up to the Commonwealth Games it could inspire many residents of this Dear Green Place."
More than 23,000 runners from 100 countries took part in this year's Edinburgh Marathon, providing a substantial tourism boost for the city.
Glasgow councillor George Redmond, who has helped organise running events in the city, said the popularity of the Great Scottish Run suggested it could be time to re-consider hosting a full marathon.
He said: "I think it is certainly time to look at this again.
"If all the factors were right, such as sponsorship and cost, I am sure Glasgow Life would consider it."
A spokesman for Glasgow Life said: "We have previously looked at staging a marathon as part of our major running events programme, but this has proved challenging due to traffic management issues and cost.
"We regularly review our running events, as shown by the hugely successful Bank Of Scotland Great Scottish Run weekend, which incorporated several new events, including the family mile, toddler dash and elite invitational mile.
"We will continue to review the programme."