The Architectural Heritage Society of Scotland has lodged a formal objection to the demolition of the B-listed London Road Primary.
Celtic FC has applied to Glasgow City Council to knock down the old school to make way for a new development.
The Society, which is a charity, believes the red sandstone school, typical of the fine Victorian and Edwardian buildings put up for children between 1873 and 1919, could be saved.
Jeremy Watson, chairman of the society's Strathclyde group, stressed such school buildings were now in danger.
He said: "The ongoing programme of school closures in Glasgow puts ever more of them at risk, yet their form allows them to be adapted to a wide range of alternative uses so that they can continue to be a valuable asset to the city for many years to come."
London Road primary, believed to be the only B-listed school in Glasgow, was closed in 2004.
It is officially owned by the council but is subject to a legal agreement with Celtic Park.
The Evening Times understands that it may be structurally unsound – making it easier to demolish. But it appears to jar with Celtic's – and, some say, the council's – vision for Parkhead to become a sporting and leisure destination.
Mr Watson believes the council should have done more to protect the building after the school closed.
He said: "The building was left sealed by the council, but not maintained as a potential asset. This is contrary to its own policy.
"If a listed building is allowed to deteriorate by a private owner, a compulsory purchase order could be sought.
"As the council itself is responsible for this one, it is responsible for the deterioration in condition.
"Deterioration in such cases cannot be considered grounds for de-listing or demolition. The condition survey documentation shows it to be still suitable for restoration and adaptation."
Mr Watson and his society, in a formal objection, said the "fine red sandstone building" could be kept as offices and should be spruced up, externally at least, for the 2014 Commonwealth Games.
Glasgow City Council as far back as 2009 said that the area around Celtic Park "does not provide an attractive setting", adding "the current situation is not acceptable with regard to the council's ambitions to host a world-class event for the 2014 Games".
Celtic have an option to buy the school but have not yet taken this up. The council and the club plan dramatic improvements to the area around the ground for 2014, including a new walkway.
Celtic declined to comment.