Last week, a panel of judges failed to agree on any of the six shortlisted schemes.
They will meet again this week and are expected to finally recommend the design they believe should get the go-ahead.
Their preferred option will have to have the support of a majority of the five strong judging panel.
It will then be voted on by city councillors who could back the plan - or opt to reject the judges' recommendation.
Insiders say that option is increasingly being talked about inside the City Chambers.
Rejecting the judges choice would leave the red-faced council with two options.
They could leave George Square as it is with its unpopular red surface or consider some other improve-ment scheme for the area.
The general view is that doing nothing is not an option as the square is now badly rundown and is not a fitting advert for a major European city.
Many members of the public have demanded the area be returned to its former glory with trees, grassy areas and flower beds.
But that option is also likely to be ruled out as it would mean public events, like the switch on of the Christmas lights which is attended by around 15,000 people, would have to be scrapped because of lack of space.
Another problem for the council is that it is determined to get the bulk of the £15million George Square facelift finished in time for the Commonwealth Games next summer.
Taking months to reach a decision on any new scheme would cut the time available to carry out the work.
Today the Evening Times is asking readers to send us details of what they want to see happen in George Square.
You can send in a drawing of your scheme or write a des-cription and get it to us via e-mail, Face-book, Twitter or in the post.
Tell us what you want for your city's main square and how you would like to see it being used in the future.
Your drawings can be outline sketches or detailed designs.
Should the statues stay or be moved to parks, should there be more trees and grass or should George Square be a Continental piazza for gatherings and events?
Send your e-mail submissions to us at news@evening times.co.uk or post them to the Evening Times, 200 Renfield Street, Glasgow G3 3QB