Wellfield Nursery in Springburn was originally based in Wellfield Public School, which was destroyed by fire in October 2005.
Pupils were moved temporarily to Balornock Primary and the unit has operated there ever since.
But the school is in poor condition and is due to undergo a major refurbishment.
City council education spokesman Stephen Curran wants to move the nursery from Balornock Primary and relocate it into a new family learning centre in the former Gadburn school, in Springburn.
The new centre, which will provide "significantly improved" early years provision for the local community will be able to provide 93 full-time equivalent places for children from birth to five-years-old.
Wellfield currently provides just 30 full-time equivalent places.
The Duntarvie pre-school assessment centre, which provides a programme for children who find it difficult to manage in a mainstream nursery, will continue to operate from a separate wing of the school.
The new centre will support families from the north of the city who have children with a range of additional support needs.
It will be staffed by NHS professionals, including consultant paediatricians, nurses and therapy staff and will offer a year round service to families.
Today, a meeting of the city council will be asked to agree to launch a public consultation on the plan to close Wellfield Nursery and move it to new premises.
Councillor Curran said: 'If agreed, this is a wonderful opportunity for the local community.
'Since the fire the nursery has been sharing accommodation and this proposal would give parents and families the opportunity to access a newly refurbished building and multi-agency services under one roof.
"I hope all interested parties will make their views known in the consultation.'
Consultation papers will be distributed to a wide range of local stakeholders and interested parties, including parents, carers and children at establishments affected by the plan, staff, the NHS, affected trade unions, community councils, area committees and other users of the school premises.
If councillors agree to consult on the plan, the consultation will start on October 1 and run until November 21. It will include a public meeting in Gadburn School.