The new building would replace the current Balmuildy Primary School which, at more than 60 years old, is one of the oldest in East Dunbartonshire. and requires significant investment to improve its condition.
It has a role of more than 300 pupils at the moment.
A report to go before the full council on 23 September lists three options for Balmuildy - a full refurbishment with a partial decant of the pupils, refurbishment with a full decant of pupils, or a new build replacement on the existing site at an estimated cost of £11.8m.
It is understood the new-build option has cross-party support and is almost certain to be signed off by the ruling LibDem/Tory administration.
Councillor Gary Pews (Lib Dem, Bishopbriggs North and Campsie) told the Herald on Monday he would be supporting the building of the new school “all the way.”
He added: ’’This is absolutely fantastic news for the pupils, staff and parents of Balmuildy Primary, and having shared the news with the Parent Council I know they are overjoyed at this development.
“I have held some surgeries in the school and it was clear to see that the fabric of the building is in a bad way.
“The repair work needed would cost almost £4 million so it makes total sense to go with the option of a new build and I will be supporting that all the way.’’
A 12-month period of pre-construction work could start next May, followed by 18 months of construction, with the new school estimated to be completed by late 2024.
The report to the council said that one of the advantages would be the site can accommodate a tandem build whilst the current school remains operational. There would also be the potential to incorporate an Early Years Facility in new building.
Joint Council Leader Vaughan Moody said: ‘’Schools in East Dunbartonshire are amongst the best in the country.
"This latest project shows the administration’s commitment to providing the very best environment in which our young people can learn and thrive.’’