At least 700 Scottish academics and another 700 non-academic staff could be made redundant if Government budget cuts go ahead.
The Association of University Teachers Scotland and the Committee of Scottish Higher Education Principals have been pleading with ministers to abandon the Conservatives' proposed spending plans in last autumn's budget for a 5.5 per cent cash cut in Scottish higher education in 1998/99.
Richard Shaw, principal of Paisley University and convener of COSHEP, said: "The arithmetic is brutal. It is pretty clear that cuts of that magnitude are likely to lead to staffing reductions."
Following meetings with Scottish education minister Brian Wilson, COSHEP and the AUTS said there were no assurances that severe cuts would be avoided.
Tony Axon, AUTS research officer, said: "We reckon it would cost Pounds 38 million to restore the cut."
The AUTS claims that Glasgow University, which is already planning 90 voluntary job losses, will be among the worst hit, facing the threat of compulsory redundancies.
But Drummond Bone, Glasgow University's vice principal, said: "The situation clearly would be serious and we've been planning for it, but we've not got to the situation where we're contemplating forced redundancies. Ways of coping would include looking at the long-term maintenance bill."
Glasgow is among the minority of institutions whose new plans to the Scottish Higher Education Funding Council are based on the 5.5 per cent cut.
The majority are not prepared to contemplate the impact publicly.
But Scottish education minister Brian Wilson said reports of impending job losses were premature and alarmist.
"I recently had good meetings with both COSHEP and the AUT at which their obvious concerns were expressed, but certainly not in such apocalyptic terms," he said. "I don't wish to see the sector talk itself down."
The short-term funding situation needed to be considered in the context of next week's report from the Dearing inquiry, Mr Wilson said.
One of Dearing's main objectives was to lay the basis for a more rational funding regime.
Mr Wilson said he had asked for a further meeting with higher educationists later in the year when final decisions were to be made.