So many international companies have said they are keen to re-vamp the civic heart of the city that the closing date for entries has had to be extended to October 26.
City council bosses are not revealing which architects want to give the historic square a new look.
But they say they are delighted – if surprised – by the response from around the world.
Councillors believe the £15 million revamp of George Square is needed as it looks tired and rundown and not fit for purpose.
It is expected the public will be asked their views about the potential designs when they have been shortlisted in December.
Council leader Gordon Matheson has said he wants the new look square completed in advance of the Commonwealth Games in 2014.
A second phase of the improvement scheme, which will involve the roads surrounding the square, will be carried out once the sporting event is over.
It is likely that all of the statues and monuments in George Square – with the exception of the Cenotaph – will be removed to allow resurfacing and other essential work to be carried out.
It has not yet been decided if some or all of the statues will be returned to the square.