Senior sources close to the selection process said it is unlikely the experts tasked with coming up with a winning design will agree on going forward with one of the current six.
The embarrassing failure to pick a winner has prompted opposition leaders in the city to call for Glasgow City Council to go back to the drawing board and recommission proposals for George Square, starting with a major public consultation.
The plans have been dogged by claims the council has rushed the process and failed to properly consult the public, with senior politicians joining many on social media sites with concerns about the process.
In an unexpected move, it was yesterday announced the jury of experts could not agree on a design. They are due to reconvene by telephone next week.
One senior source said: "If you're asking 'do I think the jury will select one of the six designs in front of it', at this juncture I'd have to say no."
Another said: "It seems the jury has reservations on several fronts.
"As we understand, two have been immediately ruled out and questions asked about the others. In short, the concern the jury has is the quality of what's in front of it and what it has to choose from.
"Both Labour and the SNP agreed George Square needs a makeover. That doesn't mean agreeing with these designs which, with the exception of the council leader and one or two notable others, have bombed both within the council and among the public.
"The jury will have asked whether making a choice is worth staking their reputations on."
The panel includes David Mackay of MBM Architects Barcelona, the ex-head of Glasgow School of Art's Mackintosh School of Architecture Professor Andy McMillan and its former head of environmental art, David Harding.
Also on the panel are DF Concerts director Geoff Ellis and council leader Gordon Matheson along with technical adviser Neil Baxter, the secretary and treasurer of the Royal Incorporation of Architects in Scotland.
Public campaigns have called for a return of much of the greenery removed from George Square in the 1990s. However, public procurement rules prevent a winner from the current options being chosen by public vote.
Any new redesign, given the timescales, would be considerably less radical than the current shortlist.
Last night, SNP group leader Graeme Hendry said the inability of the jury to select a winner was the chance to start afresh.
He added: "The process has been beyond shambolic and it is now time to go back to the start and get it right. Let's ensure the design brief meets the desires of Glaswegians and isn't obsessed with removing statutes and installing water features. Let's speak to more than 42 people when pulling the design brief together and then get the designs and genuinely consult. There is still time to get it right but we must pause now to do that.
Tory councillor David Meikle added: "This latest news that the jury can't decide and it has to be postponed, despite us being told it is time-critical, just shows what a shambles this has been.
"Labour now need to listen to the feedback from the public, elected members and campaign groups as well as take note of the petition and planned demonstration on this issue.
"Gordon Matheson needs to show leadership; start again and have a proper consultation, design and voting process which the public and councillors will have confidence in."
Mr Matheson said: "It's disappointing, but it's important that we get this right. We will make a decision next week."