Meanwhile, Cardiff University vice-chancellor Wendy Larner has emailed staff to warn there would be an immediate staff recruitment freeze.
Prof Larner said there were sufficient funds to “weather the storm” in the short-term, but it had to look for ways to cut costs.
She said there was “no need for panic”, but “we can’t continue to make less money than we spend”.
“Our financial position is not good. If we don’t take further action, then this year we stand to experience a £35m deficit, and we expect that deficit to be significantly higher next year,” she wrote.
Alongside cuts, she said the university would look at new ways to generate income.
The university said it could not rule out voluntary redundancies.
Cardiff University’s branch of the University and College Union said there were “mixed messages” from the university about the financial position and it would “enter into dispute” if there were compulsory redundancies.