Bearsden Primary School is one of a number earmarked for closure or merger under far-reaching plans for first schools in East Dunbartonshire.
Councillors are due to discuss the closure plans when they meet on Monday.
However, parents of pupils at Bearsden Primary claim other schools have more than one merger option, while Bearsden's future would be only to combine with Castlehill on the Castlehill site.
Debra Macfarlane, whose son Jack is in primary three and whose younger sons, Thomas, four, and two-year-old Charlie, would also attend, said there had been widespread disbelief at the moves.
"It was the speed of the council that really took us by surprise," Mrs Macfarlane said. "When I first heard on Monday that the school faced closure I just thought 'No, that can't be right'.
"It is not just about our school. Bearsden Primary is at the heart of the community and you have roughly 600 parents every day who are passing trade for the local shops at Bearsden Cross.
"If you close the primary school you may as well just close down the cross too."
Deborah Wallace, mother of a primary one pupil, said: "We looked for two years to buy a house in the area because the school is so good and it's where I wanted my son to be educated.
"It is such a successful school with a great headteacher and teachers – it's a such a shock to learn it might close that I didn't at first think the news was real."
Other parents said Bearsden Primary's parent council has recently raised more than £40,000 for improvements to the school playground.
Of the 13 local authorities in Scotland where the pupil numbers have reduced by more than 20%, East Dunbartonshire is the only council which has not made any reduction in the number of primary schools.
The council has published proposals affecting the future of 23 schools across the area as local councillors prepare to vote on Monday to push through the consultation. Divided into four "packages", the potential changes to the school estate come as school rolls across the local authority area are falling.
The first package, for Bearsden, covers Bearsden, Castlehill, Westerton and Colquhoun Park primary schools.
Package B covers Bishopbriggs and would see a variety of mergers between Auchinairn, Woodhill, Balmuildy, Meadowburn and Wester Cleddens primaries.
A third set of proposals, for Kirkintilloch, Lenzie and surrounding villages, affects Lenzie, Lenzie Moss, Lennoxtown, Craighead, St Agatha's, St Flannan's, Gartconner, Harestanes, Hillhead and Oxgang primaries and Merkland special needs school.
The final package covers Milngavie and would see changes to provision at Milngavie, Clober, Baldernock schools.
Council leader Rhondda Geekie said: "After the public consultation in January, which will be open to all residents and will include specific consultation exercises with our primary school pupils, the council will consider the findings and agree what packages will be taken forward."
She added: "I do think we have to emphasise this is only an informal consultation at this stage before we do a very lengthy formal consultation. We hope we can build as many new primary schools as possible to give our children the best facilities for the future."
Kenneth Brown, EIS representative for East Dunbartonshire, supported the council's proposals, saying there is a need for modern facilities to support a modern school curriculum.
Estate agent Slater Hogg & Howison, said that should the Bearsden primary building be converted into residential flats, the asking price could be between £300,000 to £600,000 for each home.