The States will vote in June on whether to let Rouge Bouillon School expand onto the former police site.
Deputy Inna Gardiner, who lodged the plans, says it's an opportunity for States members to show their commitment to the pledge to put children first.
Home Affairs Director-General Julian Blazeby told Scrutiny last month that they want the site for a joint fire and ambulance station.
He called it the most appropriate site to combine the two stations to match the current response times.
However, like many have called for over several years, Deputy Gardiner wants the school to benefit.
"If the site in question is not allocated to the School, there will be no chance of expanding the school in the future, no improvement in open spaces for the children at the school, and very limited opportunities to improve the infrastructure of the building."
The school's headteacher wrote a letter to the Public Accounts Committee last year, calling for support to give their children improved facilities and more green space.
He vented at seeing other schools benefit from new buildings elsewhere in the island without his school benefiting in a similar way.
"We have a fantastic staff and wonderful children and we do the very best we can with the circumstances we have, but surely it is not right that the children most in need of space to run about and play sport go to a school with no playing field or green space.
"We have a specialist unit for children with Autism and communication difficulties, but not a single space for parents to park in order to bring these highly needy children into school, or enable parents to meet the staff at the end of the day. We are a school that burned down about 30 years ago, but although the main fire escape has been identified as needing refurbishment or replacement for several years, the project has been
"…I have been grateful for the efforts of Jersey Property Holdings this year to paint part of the exterior of the school, and to renovate the worst of the toilets, however, these relatively small sticking plasters are dwarfed by what needs to be done to give our children the standard of facilities enjoyed by children at some of the more fortunate schools".
Around half of the children going there qualify for the Jersey Premium. Deputy Gardiner says by voting for this, it would begin to put these children first.
A written question published earlier this week revealed there has been no review of the school catchment areas in the last 15 years, with the Rouge Bouillon headteacher previously describing housing in the school's catchment area as 'some of the poorest in Jersey.'
"The Assembly have vowed to Put Children First. How can we be putting Children first when we are not prioritising their health, their education and their futures?
"The importance and urgency of this propositions purpose, to give primary school children enough room to run and play cannot be overstated.
"The time has come to act and to reallocate the site for the expansion of Rouge Bouillon school without further delay. The outdoor space, lack of playing field and green areas limits the opportunities that the pupils have to learn outdoors, to exercise, to be sociable and to play. The current state of the building in no way shows pupils they are valued.
"There is an opportunity to improve the whole learning experience at the School by providing new, updated facilities to assist in pupil development and attainment."
In the States this week, the Chief Minister said a review of the St Helier schools estate would be ready in 4-6 weeks.