The square was closed off to traffic during the recent European Championships sporting event and the council is now looking at whether or not to make the move permanent.
It is conducting a consultation to seek views on the issue.
The council stressed it was not currently conducting a statutory consultation on a traffic order.
|A number of bus services pass through the Square. Here a 398 circular service travels on West George Street towards George Square|
Pedestrianising the square could have a significant effect on businesses and the surrounding streets as well as disturbing bus transport routes which pass through the area.
George Square is one of the most prominent public spaces in Scotland. It is at the heart of Glasgow city centre and includes both the City Chambers and Queen Street railway station.
The consultation on the council's website says: "The European Championships have now finished. Alongside the sport we had two weeks of world-class culture in George Square which we temporarily closed to traffic.
"We're considering permanently closing the square and we'd like to know what you think about that."
The Federation of Small Businesses said permanent pedestrianisation could have pros and cons.
| Above, Buses that currently pass through the Square|
It is also the main operating centre for City Sightseeing
Martin Little, the FSB's area leader for the West of Scotland, said: "On one hand, this move could help make our city centre more attractive to visitors and open up the space for a range of activities. On the other, it could create difficulty for businesses that need vehicle access to their premises in the vicinity of George Square.
"While we'll ask our members what they think of the proposals, we'd urge the council to be open to any concerns raised by local firms."
Were the square to be pedestrianised, arrangements would be put in place to allow access for delivery vehicles and the emergency services - as happens in other pedestrianised areas.
Although some nearby streets would not actually be closed to traffic, inevitably closing off the square could have implications for how busy they were.
Glasgow's former Labour leader Gordon Matheson previously called for George Square to be revamped completely but faced intense opposition from critics.
The plan was dropped following an international design competition.
The council's online questionnaire runs until September. It can be found here