David Leyland, director of Southampton Institute, last week won a confidential vote of confidence at an emergency governors' meeting by what one governor called "a slim majority".
Lecturers' union Natfhe is now pushing for Professor Leyland's resignation. Spokesman Mick Jardine said: "We can't see any future for David Leyland at Southampton Institute."
Academic and administrative staff are to hold an institute-wide ballot next week which is expected to call for Professor Leyland's resignation. It will be organised by the institute's joint trade union committee, and will put further pressure on Professor Leyland, who has suffered a series of setbacks in recent weeks.
An ambitious faculty restructuring programme designed to save Pounds 350,000 has been put on ice, and the governors are understood to have warned Professor Leyland that they will not tolerate further financial losses on foreign ventures in Greece and Spain.
Governor Michael Andrews confirmed that the loss-making Southampton Solent campus in Athens - which Professor Leyland formally opened last week - could close if it does not break even next year.
The institute has already ploughed Pounds 353,000 into the Athens venture more than Professor Leyland hoped to save by an unpopular merger of the institute's key faculties.
A report by the Higher Education Quality Council, expected to be critical of the institute's overseas franchise operation, is to be discussed by governors in the next 14 days. It has been kept from governors since it was sent by the HEQC earlier this month.
Although senior managers are entitled to keep the report under wraps for four weeks prior to publication, HEQC sources said it was "quite extraordinary" that Professor Leyland had not let governors see the report.