Glasgow City Council, which awards safety certificates to both Celtic Park and Ibrox, said it was not in the public interest to publish details of the issues discussed at meetings with Celtic and Rangers.
But terror experts claim non-disclosure of the information is part of a wider trend of public authorities using security concerns as an easy option to curtail inquiries often in the public interest.
Amid much speculation about the safety of both grounds, which can host up to 110,000 people on any given weekend, the authority said there were currently no issues with the structural integrity of either stadium.
It also said the decision last month by Celtic to shut a section of the stadium occupied by the notorious Green Brigade "had been taken by Celtic Football Club of its own initiative", but that given ongoing concerns about safety it believed the closure decision to be "a proportionate and reasonable response by the football club".
The Herald requested under Freedom of Information legislation all correspondence between the council and Celtic and Rangers regarding the renewal of stadium safety certificates, as well as minutes of meetings.
However, the request was refused on the grounds that disclosure of the information would, or would be likely to, "endanger the physical or mental health or the safety of individual spectators at the stadium".
The responses from the council's chief executive's department, said: "Given the high-profile nature of both stadia there is realistic potential for information relating to safety and security arrangements to be utilised in the perpetration of an act of terrorism or similar malicious act and, therefore, endanger the physical or mental health of the spectators.
"On balance, the council is of the view that the risk of information being use for malicious purposes that could realistically endanger persons outweighed the public interest in the release of this information."
Professor Stephen Vertigans, head of the School of Applied Social Studies at Robert Gordon University in Aberdeen, said the chances of any terrorist attack on the stadia was extremely remote.
Professor Vertigans, who has written extensively on terrorism, added: "In the past decade or so there's been a trend of public authorities using new powers they've been allocated.
"Groups concerned with civil liberties are increasingly worried about how this legislation is applied, what is in the public interest and how that is dominated by security concerns.
"The lack of transparency in that process does raise major concerns. It's used as the easy option and is a deterrent to exploring and public understanding."
Dr Andrew Sanders, a research fellow in Diaspora, Conflict and Diplomacy at University College Dublin, said: "In my own view, it seems a little sensationalist to deny access to information regarding public safety on this basis. Football stadiums are considerably safer than they were in the mid-1980s, but fan safety needs to be continually scrutinized in order to ensure high standards are met."
In August, soon after having its safety certificate awarded for a further 12 months, Celtic closed section 111 in its ground, which is used by the Green Brigade, claiming it had been "left with no option", referring to the inability to operate without the consent of the council.
But the authority said: "For the avoidance of doubt, it is the management team of any football stadium in Glasgow that has ultimate responsibility for the safety of their spectators."
A council spokesman said it had refused several requests for the information on the same grounds.