Worried mums and dads have been warned that Hillhead Nursery could close and children moved to give more space to Hillhead Primary.
At a meeting with executive director of education, Maureen McKenna, parents were told the nursery could close to ease pressure.
One mum, who asked not to be named, said: "The information we have been given so far is vague. We have been told the nursery could close and the children relocated to other nurseries, or that it could move to another site.
"Even if they move the nursery that's still essentially closing it. After all, we wanted out children in the new building. It's why we put them there."
The plan is revealed in a briefing note from the Hillhead Primary Parent Council, seen by the Evening Times.
It states Glasgow City Council could: "Carry out an informal consultation about moving the Early Years Centre (EYC) and use these rooms for the school.
"This would provide two classrooms, one room which is too small for a classroom and toilets... with the possibility that these rooms may be available by August 2015."
The nursery currently caters for 79 two to five-year-olds and opens 8am to 6pm.
The new Hillhead Primary opened in 2011 after a merger of the former Hillhead Primary with Dowanhill, Willowbank and Kelvinhaugh schools.
Inaccurate projections meant the school reached capacity faster than planned, with 130 new pupils joining in just two years.
To make space for the extra pupils, general purpose rooms have been taken over for use as classrooms.
Parents also have concerns that there are now too few toilets.
The school has lost its dedicated art, music and media rooms and there are plans to convert its library into a classroom.
In January we reported that Hillhead could have its catchment area redrawn to deal with the problem.
Families living in the catchment area were told they no longer have an automatic right to a place for their children.
The school, built to take 632 pupils, already has 649 on the roll and this is likely to rise to 678 by August.
The briefing note says lack of space is restricting drama, art and music teaching, gym time and is putting pressure on the dining room and playground.
It is understood that the Parent Council is now in talks with Glasgow City Council.
A council spokeswoman said: "We have been engaging with parents about the capacity at Hillhead and will soon be consulting on the potential solutions, such as reviewing the catchment area and nursery provision."
She added the council is committed to continuing to provide nursery provision in the West End.