Dundee City Council is set to spend £122,500 on asbestos removal at Rockwell High School.
The substance was discovered in the attic space and in “other locations” during maintenance work on the school’s heating system in the winter of 2015.
City councillors will be asked on Monday to agree to pay for it to be removed in August and September this year.
Labour’s education spokesman Laurie Bidwell said he was concerned the work could be carried out while staff and pupils are likely to be in school.
Pupils and staff from Harris Academy have been in the old building since work on the new Harris commenced.
They will move out at the end of summer term, but a recent report before councillors said staff and pupils from Castlepark and Balerno off-site centres will move to Rockwell in August 2016.
MR Bidwell said: “I don’t think we should have any staff or pupils on site while the asbestos is removed.”
Jimmy Black, SNP councillor for the area, said the asbestos would only pose a health risk if it was disturbed and the council has “some expertise” in removing it from old buildings.
A council spokesman added: “The city development committee will be asked to agree to appoint specialist contractors to remove asbestos from a roof space in a part of the school that will be unoccupied.
“Pupils currently using the school will return to Harris before the work is carried out later in the year. Part of the former Rockwell site will be used as a base for specialists education provision, while no decisions have been taken yet about future uses of the rest of the site.”