Kelvin Park Early Years Centre could close to make space for more classrooms for the adjoining Hillhead Primary School.
But nursery parents said an overcrowding issue at Hillhead is temporary and their nursery should not be sacrificed.
Campaigner Kate Cotter said: "For children it's about continuity but, also, this would be devastating to the quality of family life as parents can't take their child to a nursery in one place and then a separate primary school.
"If you have a third child in secondary school then it becomes a kind of joke."
Kelvin Park is the only council-funded EYC in the west end of Glasgow providing full time child care 52 weeks a year. Closing it would mean moving 120 children.
Hillhead Primary and Kelvin Park opened in 2011 with pupil numbers increasing rapidly to capacity.
To deal with the issue of overcrowding, Glasgow City Council has issued a consultation document that proposes changes to the Hillhead catchment area.
It also proposes closing and moving the children and staff of Kelvin Park to six different nurseries to make space for two classrooms and a general purpose room.
Children would be moved to Cowcaddens Nursery, Woodside Nursery, Cranstonhill Nursery, Oakgrove Primary, which does not currently have a nursery but does have a spare classroom and Elie Street Nursery.
Only two of these offer 52-week opening hours.
Local politicians, including the Green's Nina Baker, MSP Hanzala Malik of Labour and SNP councillor Ken Andrew, have given their support.
Mr Malik said: "It would be a horrible situation if this learning community was scattered to the four winds even on a temporary basis."
Mr Andrew added: "I can only hope that a sensible and pragmatic solution can be found to preserve the nursery while finding the extra accommodation that Hillhead Primary clearly needs."
And Ms Baker said: "As the problem is temporary so the solution should be temporary, namely portable classrooms for a couple of years."
Councillor Stephen Curran, executive member for education and young people, said; "It's important to highlight that at this stage no decision has been taken to close Kelvin Park Early Years Centre.
"We are undertaking an extended public consultation and Education staff are seeking the views of as many interested parties as possible."