Kincardine Nursery School is part of the Avenue End campus, along with Avenue End Primary and Croftcroighn Primary.
The East End nursery provides 15 term-time morning and afternoon places for two to three-year-olds and 60 term-time morning and afternoon places for three and four-year-olds.
However, Avenue End Primary is experiencing an increase in pupil numbers because of the rising birth rate.
To cope with demand, temporary accommodation has been provided to allow the school to look after all the children in its catchment area.
Garthamlock Family Learning Centre, which is across the road, shares its campus with St Rose Of Lima Primary.
The learning centre provides early years education and childcare for youngsters from six weeks to age five and is open all year round.
St Rose Of Lima is also having to cope with increasing pupil numbers.
Tomorrow, education bosses will ask councillors to agree to consult on plans to move the pre-school youngsters from Kincardine Nursery and Garthamlock Family Learning Centre to a new building nearby.
That would allow Avenue End Primary and St Rose Of Lima Primary to use the buildings, both of which are only seven years old, to cope with their rising pupil numbers.
A report from Maureen McKenna, the city council's executive education director, said: "Should the proposal be agreed, children who attend both nurseries will be offered a continued placement at the new nursery or an alternative nursery based on parental choice.
"The new nursery would have an increased capacity to meet the anticipated demand for placements.
"In addition it will offer new provision for very young children."
It is planned the new nursery will be open all year and will provide 12 places for under two-year-olds, 40 for two to three-year-olds and 88 for three to five-year-olds.
If the scheme gets the go-ahead, it is hoped it will be ready during the 2015/16 session.
A wide range of people and organisations will be consulted on the plan. They include parents, carers and children, staff, other local authorities, the health board, trade unions, community councils, area partnerships and other users of the school premises.
If councillors agree, the consultation will begin on April 22 and there will be a public meeting in Avenue End campus on April 30.
The council also intends to consult on plans to close Rosevale Primary, a special needs school in Milton, which has been lying empty since last August. Pupils have been given the support necessary to allow them to attend mainstream schools.