David Meikle, who represents Pollokshields, says the panel is not representative of the city because it contains no community members and no women.
Mr Meikle believes the new design should be chosen by a group that better represents the city.
He said: "It is outrageous that the jury is all male and does not include any women or community representative.
"The question must be, who appointed the jury? The jury will make the final decision on what design wins. Councillors or the public only have a few days to give feedback on the designs.
"Sadly, this, along with the poor consultation process, which involved a survey of just 42 people, has turned the whole George Square redesign project into a farce."
As reported in the Evening Times earlier this week, a panel of five will choose one of six designs to transform the Square.
They are David Mackay, a partner of Barcelona- based MBA Architects; Professor Andy McMillan, former head of the Mackintosh School Of Architecture at Glasgow School Of Art; David Harding, former head of environmental art at Glasgow School Of Art; Geoff Ellis, director of DF Concerts; and city council leader Gordon Matheson.
The six final designs – now on display at the Lighthouse in Mitchell Lane – were chosen from 30 submitted entries.
A public consultation was held to whittle the 30 down to six and involved an Ipsos Mori survey of 42 people and seven 'stakeholders'.
Mr Meikle added: "What was a laudable project is now at a stage where the council needs to have a rethink before any final decisions are made, especially as £15m of public money is at stake.
"For me, the best thing to do is to let the people have their say."
A council spokesman said: "Recommendations from council officers, who put forward the names of recognised experts in their fields, all of whom have an in-depth knowledge of and love for Glasgow, determined the make-up of the judging panel."
The winning design will be announced on January 18.