University of Wales Trinity Saint David has written to all teaching and support staff asking for them to consider voluntary redundancy.
The university said it needed to cut staff costs following a review and rejected claims by union Unison the reductions could affect 10% of the 1,500-strong workforce.
It has campuses in Carmarthen, Swansea and Lampeter.
A university spokesman said: "As part of its normal ongoing business practice, the university regularly reviews its staffing costs in line with sector benchmarks.
"The university's current staffing costs are above sector benchmark comparisons and therefore a review of staffing levels across all academic and professional units is being undertaken."
He added the university had met with unions to inform them of the process, which is due to take place over the next few weeks.
The announcement comes with work already under way on the first phase of a Â£300m development at Swansea's SA1 waterfront site.
Hugh McDyer, from Unison, said: "We know there are big changes ahead at the university and a likely merger of sites.
"We'll work with them to identify savings, if they need to be made, but that should not be at the cost of frontline workers.
"It is essential the quality of learning and student support is protected and we want the University of Wales Trinity Saint David to be open and honest about the scale of the challenge it faces."
The university has denied the cuts will affect 10% of staff and any possible merger of sites.
It followed Thursday's announcement by the University of South Wales of plans to cut 139 jobs.
A Welsh Government spokesman said: "We are aware of the situation at University of Wales Trinity Saint David.
"We would expect for there to be a period of consultation, and that staff and unions are kept informed at all stages in the process."
A second south Wales university has announced potential job cuts.