Local people are campaigning to get the Winter Gardens restored and reopened to the public.
But the city council says it is not able to fund the £800,000 cost of the work.
Instead, the glasshouse will be covered in a £60,000 wrap which will show how it will look when work is carried out.
That will help preserve the fabric of the building which is currently covered by scaffolding and improve the area in time for the 2014 Games.
Tollcross International Swimming Centre will be one of the key venues for the sporting extravaganza which will be seen by £1.5billion people around the world.
The Winter Gardens underwent a £1.9m refurbishment between 1998 and 2000 which was funded by the council in partnership with the Heritage Lottery Fund and Historic Scotland.
That allowed the building to be reopened after being closed for 14 years.
However, the B-listed Victorian greenhouse was forced to shut again in 2011 following two major storms.
Campaigners have been fighting for money to be found to carry out the necessary repair work.
Members of Tollcross Walking Group have now raised the state of the building with the city council's petitions committee.
Their petition read: "The Winter Gardens, a beautiful Victorian glass structure, is in a state of disrepair and is an eyesore.
"We were led to believe the Winter Gardens was closed for renovation yet we see no work being undertaken.
"Given that next year sees the Commonwealth Games coming and many events happening within the East of Glasgow, it would be an added bonus to see the Winter Gardens restored to their former glory for visitors and for the people of Glasgow."
Alison Lawson, a member of the walking group, told members of the public petitions committee that the Winter Gardens are presently an eyesore.
She said: "It is a beautiful Victorian structure which is currently in a state of disrepair. It is a monstrosity which is falling apart and has scaffolding round it.
"The Winter Gardens are bound up with the history of the East End of Glasgow and its people and needs to be saved for future Glaswegians."
George Gillespie, depute director of land and environment, said the building was closed as its condition had deteriorated raising health and safety concerns.
He added: "We took a decision four years ago to close one part to the public but following that there were two major storms.
"The porch began to move raising the danger of the glass falling out and the whole structure was vacated.
"At this stage we are proposing to put a wrap on the building to make it more aesthetically pleasing for people who use the park.
"And our officers will work with any community groups to develop a business case to get some investment into the gardens."
Mr Gillespie stressed whatever plan is drawn up must be financially sustainable but added: "Without doubt, we would like to see this garden back into play."
The future of the Winter Gardens has now been referred to the sustainability and the environment committee chaired by local councillor Frank McAveety.
He said: "I am really keen to see to see investment to bring the glasshouse back up to standard.
"I want to work with residents to make sure the Winter Gardens can be sustainable for the future."