The local authority's own internal auditors have warned that failure to keep comprehensive records means they can't be sure all premises have been checked for the material.
In what opposition leaders said was a "damning report", the watchdogs also revealed that policy on how asbestos is managed in Glasgow is more than a decade out of date.
The auditors, in a series of recommendations for the council's spin-off buildings landlord City Property, called for the asbestos monitoring system Modus to be kept up to date.
They said: "City Property does not have a comprehensive list of all properties.
"As such the auditor cannot be assured that all properties have received an asbestos survey.
"City Property does not receive notification of all asbestos works.
"The Modus system information is incomplete and out-of-date (for example, demolished schools are recorded as 'in use'), increasing the risk that not all relevant properties are covered by the asbestos review process."
The auditors, who were reporting to a meeting of the council's Finance and Audit Scrutiny Committee this week, also found that the city's policy on asbestos management had not been updated since 2003.
They said: "As such there is a risk that not all the parties involved in the process are aware of their responsibilities."
They have now called for a single asbestos tsar to be appointed in the council to ensure that the local authority - and its network of arm's-length external organisations or Aleos, such as City Property, keep on top of the issue.
They have also called for a central register of all recommendations from asbestos surveys to be put in place by the end of this month. Work is already in progress.
Opposition leader Graeme Hendry of the SNP said: "This is a damning report into the management of asbestos in council properties.
"The council policy is more than 10 years old and no-one has overall responsibility for management of this potentially deadly substance.
"The council appears to have an incomplete and outdated list of affected properties - the report cites the case of former schools, now closed, recorded as 'in use'.
"Have these buildings been sold on, or demolished? What steps, if any, were taken to deal with the asbestos risk on site?
"The report makes five recommendations, four rated as 'High' priority, covering issues such as management, policy, recording of affected buildings and communication between departments and Aleos.
"The council must urgently get a grip of this situation.
"My group will continue to pursue this issue, to ensure the safety of all those who live and work in Glasgow."
Councillors will discuss the report, but the Evening Times understands work is already well under way to fix some of the problems raised.
A spokesman for the council said: "We audit our processes and procedures because we want them to be as robust as they possibly can.
"In this case, we found weaknesses in the way we share and record information about some of our estate and, quite rightly, those are being challenged and improved as a matter of priority.
"It is important to be clear that, while these weaknesses posed a risk to the council itself, they did not present a danger to the physical health of the public or staff."