The university currently employs more than 3,000 people.
Prof Gillespie told staff: “We must take further action now to address our financial stability and long-term future.
“Given the profile of our costs, it is inevitable this will mean a reduction in our staffing levels.
“This will be a very difficult period, certainly for this financial year and next.”
One staff member told BBC Scotland News: “The freeze on staff recruitment and the non-filling of vacancies will over-burden an already demoralised staff, and the threat of redundancy makes things even worse.
“Staff who are on precarious temporary sessional contracts will be the most affected by this initially.
“Whilst most staff care about the students and go that extra mile to help, as always, the students will feel the effects of this the most.”
