Universities in England face funding cuts of ÂŁ4.2bn in the coming Spending Review, an e-mail leaked to the BBC News website suggests.
Universities UK head Professor Steve Smith wrote to vice-chancellors saying this week's Browne Review set out figures that "confirm our worst fears".
He says they signal cuts of ÂŁ3.2bn from teaching and ÂŁ1bn from research in next week's Spending Review.
The government said it could not comment.
This is because the Department for Business, Innovation and Skills says it does not know what is in the Chancellor's spending review plans.
In his letter to fellow vice-chancellors, the UUK president suggests the impact of the Spending Review will be more important than Lord Browne's review of fees published this week.
This is "because potential cuts have been getting worse and worse", he says.
He continues: "Browne explicitly says that Hefce (England's university funding body) will have teaching funding of ÂŁ700m; the current sum is ÂŁ3.9bn.
"This implies a cut of around ÂŁ3.2bn in state funding."
This would represent a 79% cut in the teaching grant.