Leeds is one of seven regional centres affected by the plans announced yesterday.
The University and College Union says that almost 500 jobs could be at risk nationally.
However the Open University (OU) said that it did not expect the proposed change to result in any compulsory redundancies.
The OU is proposing a new structure which would see regional offices in Leeds, Bristol, Birmingham, Cambridge, Gateshead, London and Oxford close.
An OU statement said: “We do not expect this proposal to result in any compulsory redundancies, but expect that affected staff would need to relocate, or take voluntary severance or early retirement.”
If the plan is approved, the OU would retain offices in Belfast, Cardiff, Edinburgh, Milton Keynes, Manchester.
The OU statement said: “The university has almost 200,000 students, with many combining their study with employment and other commitments.
“This means our students have unique requirements in terms of accessing support, including the need to contact our teams outside of normal working hours and getting prompt answers to their queries. The proposed new larger three centres in England, together with our National Centres in Belfast, Dublin, Cardiff and Edinburgh, would allow us to invest more in student support and deliver improvements that are not possible in the current configuration of 13 offices.
“These improvements include quicker response times, more proactive support to those students who need help during their studies and longer opening hours.
“The larger centres will help us provide seamless support for students from first contact through to completion of studies.”
Vice chancellor Peter Horrocks, added: “The OU’s mission has always been about embracing innovation and providing our students with the best possible experience. With developments in technology changing how we work, the student’s experience of the OU has not been limited by geography for some time. This is a difficult decision and I fully recognise the impact it will have on many of our staff, but we cannot afford to stay still.”
However the UCU has hit out at the plans. The union said staff in Leeds would have to travel for around an hour to reach their nearest centre in Manchester.
The union said to lose “huge amounts of expertise would be a devastating blow” and questioned why so many centres were being hit at the same time. It said staff in the local offices evaluate and support students with disabilities, provide course materials and assign tutorial groups.
Open University UCU branch president, Pauline Collins, said: “The Open University is respected the world over for the way it brings quality higher education to a wide range of people.
“At the core of that mission are its dedicated regional staff who provide essential support to thousands of students and their tutors. Axing almost 500 staff across seven centres would be catastrophic and decimate the Open University’s ability to provide the kind of local support that students need.
“We are unconvinced by the university’s talk of staff relocating.”