The university, which employs 8,606 people, is also reviewing infrastructure projects as it looks to tackle the shortfall.
Recently released Home Office figures show the number of international students applying for visas to study in the UK had dropped.
The University of Sheffield said staff had been told about some of the cost-saving measures it was taking, alongside “seeking to protect the excellent work that takes place across the university”.
“We are continuing to speak to the government about the value our research, innovation and education brings to the UK economy, and hope to work together to find solutions to the funding challenges facing higher education,” a university spokesperson said.