Sir Menzies, who is chancellor of the University of St Andrews, told Times Higher Education that a number of his Lib Dem colleagues shared his view that he would "lose all credibility" by reneging on a pre-election pledge on the issue.
The party's position has been superseded by the coalition government agreement struck with the Conservative Party, which leaves Lib Dem MPs free to abstain from any vote to increase fees but not to vote against a rise.
Sir Menzies' comments came as simmering political tensions over fees, university places and funding boiled over after David Willetts' first major speech on the sector.
Speaking at Oxford Brookes University last week, the universities and science minister said that Labour had left higher education on "shaky financial foundations" and indicated that supply-side reform was a necessity.
However, Mr Willetts' key messages were almost drowned out by a row over his comments in the national press that the cost of degrees was a "burden on the taxpayer".
The remarks were seized upon as evidence that the Tories will endorse any recommendation to raise the fee cap made by the ongoing funding review led by Lord Browne of Madingley - a potential coalition-wrecking issue.
The week before, Simon Hughes, the new Lib Dem deputy leader, said that opposing fees was the 'right thing to do' and that the party voice would be "loud and clear" on fees, there is a growing feeling that some will break ranks.
Sir Menzies told THE he could not ignore the pre-election National Union of Students pledge, signed by all Lib Dem MPs, to vote against a rise in fees.
"I think it would drive a horse and cart through my credibility in my capacity both as chancellor and as an MP if I were to renege on that pledge - and I don't intend to," he said.
"I haven't done a headcount ... but I think a number of colleagues have expressed informal sympathy with my view."