Bedfordshire University, which makes about £25m a year from fees from foreign students, says it lost £10m last year due to a two-month freeze on student visas.
The university said it had started a voluntary severance scheme, giving staff up to 20 April to apply to leave.
A union called for the university to find "alternative" savings.
University vice-chancellor and former Labour minister Bill Rammell, who receives a remuneration package of £251,000, said he did not think there would be a need for compulsory redundancies.
"By making planned and sensible reductions, the university aims to continue to drive forward enhancements to facilities, to the benefit of students," said a unversity spokeswoman.
The university has campuses in Luton and Bedford.
A spokesman for the University and College Union (UCU) said: "The University of Bedfordshire needs to continue working with UCU to identify alternative savings and avoid redundancies where possible."
A university has asked its 1,400 staff if they want redundancy as it looks to make 50 job cuts to save £2.5m.