Akiva School in Finchley is hoping to purchase and refurbish the adjacent building to make space for third-form entry.
Philip Simmons, chairman of the school's foundation, said that high demand had persuaded governors to attempt to buy the next-door beit midrash from the Movement for Reform Judaism.
"We have always had considerable demand and we have to disappoint large numbers of parents and children each year.
"The opportunity has come up to acquire the building next door and if we can fund that it would be entirely suitable for a third form. There is no other possibility of expansion on the current site.
"Hopefully the negotiations with Barnet will be resolved in the next few months. When we get funding in place, we'd have to have planning permission before anything could start."
A council spokesman noted "a high demand for primary school places across the borough, including within our many faith communities.
"Akiva School has put forward a proposal to the council to investigate whether any funding is available to refurbish a building they are hoping to purchase.
"The council is in discussion with the school about this as part of its wider strategy to expand the number of school places available across Barnet, but no decisions have been made."
Akiva currently has 328 pupils. "This will grow by 30 per annum to a maximum of 420 when the two-form entry is full, in 2012," Mr Simmons explained.
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