The School of Music at the University of East Anglia could be forced to close after funding shortages triggered a rethink of degree subjects.
A panel of senior academics stated in a report that the school could not meet the "scale of demands" now being imposed on universities.
Seven full-time jobs would be at risk if the closure was to go ahead.
The report recommending the move will be put to the university's governing council on 9 November.
A final decision is expected on 28 November.
If it was to close, the school's 149 students would be allowed to finish their degrees, with the last to be completed in 2014.
The review notes that it would be difficult to expand student numbers at the school, saying it would require the university to divert resources from other departments - possibly putting them at risk.
The university's vice-chancellor Professor Edward Acton said: "In a harsh and increasingly competitive and market-focused environment, these are steps that UEA cannot afford to take.
"What makes this position especially painful is the knowledge of the school's fine achievements.
"Whatever is decided, we are determined to ensure that current students in the school are strongly supported and are able to complete their studies successfully."
Professor Tom Ward, the university's pro vice-chancellor, said there was a "strong aim to minimise redundancies" and talks would be held with staff affected.
The School of Music, which began its work in the 1960s, was one of the first schools to be opened at the university.
It had academic links with the late East Anglian composer Benjamin Britten.