And when the judges instead picked a design that Gordon Matheson strongly disliked, he scrapped the project in what the sources described as "a fit of pique".
Although the chairman of the judging panel was officially David Mackay, a partner in MBM Architects Barcelona, the Sunday Herald has been told by two sources that Matheson made it clear at the first meeting that he would be de facto chairman as he was council leader and the redesign was his brainchild, adding that public opposition would not affect the outcome.
The sources say Matheson then appeared to pre-empt the judging process by saying he thought Option 6, by architects Burns & Nice, should win. He also openly criticised Option 2, by John McAslan & Partners, sources said.
However, when the results came in, on Thursday, January 17, they showed the McAslan design was the winner. Matheson's preferred option came fourth.
Matheson "had his head in his hands", according to one council source.
There was then a break over the weekend, and when the judges reconvened last Monday, the McAslan design was formally signed off as the winner, resulting in jubilation at the practice.
But within moments, as the judges and council officials relaxed at the end of the process, Matheson informed them that his administration would not proceed with the redesign after all, and there would be a vague "facelift" to remove the old red tarmac instead.
"It was disappointing, frustrating and a lost opportunity," said one of those intimately involved in the design contest.
Another senior source called it "a bombshell".
Matheson then issued a press release saying public opposition had driven the U-turn.
He stated: "The people of Glasgow have made it clear that they do not want a radical redesign - I am proud that I am listening to them."
But well-placed council sources claim Matheson had, in fact, "thrown his toys out the pram" and "pulled the plug in a fit of pique because he lost".
One senior council source said: "Cllr Matheson had an idea, included it in his manifesto, and then decided that it was his way or not at all. It's a flagrant waste of public money and of everyone else who was involved in the process. People should have been advising against this disregard of due process."
Another senior source said: "It's been a farce."
A Labour councillor described the design contest as "a f***ing disaster" for Glasgow, adding: "It was all vanity stuff. Matheson probably wanted his name in George Square somewhere. It's like Carry On Council sometimes. You couldn't make it up."
The aborted exercise is expected to cost taxpayers up to £100,000, with all the firms who applied to revamp the square racking up about £250,000 costs.
Opposition parties last night called for the spending watchdog Audit Scotland to investigate.
Matheson's judgment is already in the spotlight after it emerged that police had reported him to prosecutors over an alleged public sex act with another man in a car near his home. No action was taken after prosecutors concluded there was "insufficient evidence" of a crime.
Matheson said the alleged incident, in Glasgow's southside last month, had exposed "an affair" and apologised to his civil partner, Stephen Wallace.
There has been speculation that Matheson pulled the George Square project because he felt too weak politically after the news broke to cope with any level of public hostility to the plan.
Matheson kick-started the George Square revamp process in April last year when he included a pledge in Labour's manifesto to upgrade the square as part of preparations for the 2014 Commonwealth Games.
However, a £14,000 focus group exercise by pollsters Mori for the council in August found public appetite for a radical change was "at best lukewarm".
Although people wanted the red tarmac removed, they were worried about costs, loss of statues, and the potential loss of grass and flowerbeds.
Despite this, the council pressed ahead with an international competition in September, with the design brief discussing radical changes such as the removal of all the statues bar the Cenotaph, removal of flower beds, and a new water feature.
After 35 entries came in from around the world, six were shortlisted in November, and Matheson praised their "international experience".
On January 9, when the six shortlisted designs went on display, Matheson insisted the public were behind the changes, despite a growing campaign to save the statues and abandon the overhaul.
The judging panel was: Matheson; David Mackay, a partner in MBM Architects Barcelona; Professor Andy McMillan, former head of the Mackintosh School of Architecture in Glasgow; David Harding, former head of environmental art at Glasgow School of Art; and Geoff Ellis, director of promoters DF Concerts.
Graeme Hendry, leader of the SNP opposition in Glasgow, said: "Cllr Matheson was obsessed with turning George Square into his own personal legacy and showed no regard for the public or taxpayers' money. It would now seem that once it became clear the panel didn't support him, he threw the whole project out in an act of petulance. Cllr Matheson's waste of over £100,000 is a matter I would expect to require further investigation."
Conservative councillor David Meikle said Matheson's "childish behaviour" had cost taxpayers dear.
"It's now proper that this is investigated and Audit Scotland may be the most appropriate body to look at it. We know it's a red square, but the council leader doesn't need to act like a tsar."
A Glasgow City Council spokesman said: "It became clear over the course of the process that there was no public support for a substantial redesign and whatever design had been picked would not be being implemented."