First Minister Nicola Sturgeon has said she would prefer to have "more teachers, not fewer", amid reports 800 could be cut in Glasgow to save money.
The Daily Record, reporting on a leaked document on Thursday, said SNP-run Glasgow City Council is also considering shutting primary schools early on Fridays in a bid to save £51 million from its education budget.
Teaching unions said they are "desperately worried" about the proposals, warning they would have a detrimental impact on the city's young people.
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Glasgow City Council is facing a £68 million shortfall for the year ahead and will set its budget next month.
The document seen by the newspaper says £22.5 million could be saved by revising the way primary and secondary schools are staffed, which would affect pupil/teacher ratios and lead to many more composite classes, with 397 teaching posts affected.
A proposal to cut the number of teachers by closing schools early on Fridays, affecting 324 roles, would save £18.5 million.
If all the options for cuts came into force, around 800 teaching posts would be at risk, as would the roles of more than 100 "support for learning" staff, the Daily Record reported.
When confronted about the leak during First Minister's Questions by Scottish Conservative leader Douglas Ross, Ms Sturgeon sought to downplay it.
"This, of course, is that time of year when we get lots of reports about savings options that different councils are considering and opposition parties - quite understandably - make hay with that, but very often these proposals do not proceed," she said.
"I think the official report of Parliament will be littered with examples of what I've just spoken about.
"In terms of these particular proposals, I've not seen the detail of these.
"Councils of course are autonomous in their areas of responsibility, something that parties across this chamber often call on the Scottish Government to respect.
"But as my record shows and indeed as Government's funding to councils demonstrates, I am in favour of more teachers, not fewer teachers."
Mr Ross said the First Minister's record is 900 fewer teachers in 2022 compared to when the SNP took office in 2007, but the figure increased from 50,576 in 2015 - the first full year of Ms Sturgeon's tenure - to 53,337 last year.
He said: "She's saying I'm standing here making hay - no I'm not, I'm deeply worried that one of the biggest councils in Scotland is considering 800 teachers being lost."
The First Minister said the Scottish Government has provided a real terms increase of £160 million for local government in the budget.
But council umbrella body Cosla said last month services could be "at breaking point" and suggested the cash increase could be just £71 million as a result of ring-fencing.
Susan Quinn, Glasgow local association secretary of the EIS teaching union, warned the proposals would have a detrimental impact on young people's life chances.
She told the PA news agency: "We are desperately worried about the impact of cuts on the ability of teaching staff in the city to deliver for the most vulnerable of young people.
"Eight hundred jobs is about 12% of the teachers in a city where young people already have some of the highest challenges to overcome to progress in their lives."
She went on to say the changes being considered to primary schools "beggars belief", adding it "makes no sense" and would impact on the ability of teachers to deliver for pupils.
Seamus Searson, general secretary of the Scottish Secondary Teachers' Association union, said young people need more support, not less, as they deal with the impact of the pandemic on their education.
He said: "If you start cutting back the number of teachers, you are really damaging education. After the pandemic we are still in the stage of recovery and a lot of youngsters have missed out on basic learning coming through.
"If you cut teachers, you are cutting young people's life chances down."
A Glasgow City Council spokeswoman said: "As part of the annual budget-setting process, a cross-party group of councillors works with officers to scrutinise and develop options on where savings and investment could be considered.
"Officers also regularly update a financial forecast, taking into account inflation and the latest information on national settlements.
"The financial challenge facing the council this year is exceptionally tough, with savings of around £68 million required, even before pressure on social work and care services are taken into account.
"Political groups will present their budget proposals next month and it is for them to decide whether they wish to include any of these options."
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