The perfect spot for Brookline’s new elementary school has proven elusive.

But the town is inching closer toward finding a location that poses the fewest challenges to building the new classrooms officials say are needed to accommodate unrelenting enrollment growth.

A consulting firm will be hired to perform a feasibility study and come up with concept plans for three sites: the Stop & Shop on Harvard Street, and school-owned land at the Baldwin School in Chestnut Hill and the Baker School in South Brookline.

The town has set aside $800,000 for the site planning and is in the process of selecting a consulting firm to begin the work this spring, with a report expected by fall.

Cottage Farm in North Brookline and Larz Anderson Park had been considered the top contenders when town and school officials singled them out for “additional due diligence and review’’ last fall. Both have since fallen out of favor, however, because of legal restrictions on the land at Larz Anderson and wetland issues and historical district challenges at Cottage Farm.

Another location, at the Putterham Golf Course, favored by a vocal group of parents in South Brookline, appears to have been ruled out.

“For all practical purposes, the golf course is off the list at this time,’’ said Neil Wishinsky, chairman of the Board of Selectmen. “It’s just not practical.’’

That property falls under the purview of what’s known as Article 97, a state law passed in 1997 to protect recreation and conservation land from being developed or used for other purposes. Using the land for a school would require unanimous approval from the Recreation Commission, among other things, and commission members have said they oppose the idea.

While Wishinsky ruled out the golf course, School Committee chairwoman Susan Wolf Ditkoff said she won’t definitively eliminate any potential sites until a suitable location has been found. “Until we have a final site we can’t make any promises,’’ she said.

“Everything will be hard, everything will be expensive,’’ she said. “But at the end of the process we will find a way to come together as a community and build a great school.’’

Ditkoff said the consulting firm will examine environmental factors at each of the top three sites, conduct preliminary traffic studies, and come up with concept plans for what could be built at each location.

At the Baker School site, for example, there are several options that could be considered. A second separate elementary school could potentially be built on the site, a significant addition could be added to the school that is already there, or an attached elementary school could be added with a shared cafeteria.

A second school could also potentially be built and the grades split between the buildings, with kindergarten through fourth in one building and grades 5 through 8 in the other, Ditkoff said.

The Baldwin site may be the easiest on which to build, according to Wishinsky, but the location is not the best for an elementary school and would require busing a significant number of students.

He called the Stop & Shop option “very interesting and potentially exciting from an urban planning perspective.’’

It is also the only one of the three that would not require taking open space for the building.

This option would require purchasing or leasing land at the Stop & Shop property on Harvard Street, and probably the gas station and car wash next door, and could involve building a school next to the Stop & Shop or as a mixed-use building with the grocery store. In any scenario, Wishinsky said, keeping the supermarket is a must for the neighborhood.

“We don’t want to constrain the process,’’ Ditkoff said. “We want [the consultants] to take a look at the sites and give us their own professional, architectural judgment of how it could work.’

School officials say that with steady enrollment growth, which has added more than 1,000 students to the schools since 2010, the average class size will increase from the current 21 to 24 students in the fall of 2020 without new classrooms.

That average class size of 24 students in 2020-21 would also mean classes throughout the system ranging in size from 20 to 31 students, with 70 classes of 25 or higher, according to figures on the Public Schools of Brookline website.

Classrooms can be added using modulars, rented space, and “substandard’’ space within schools on a temporary basis, according to officials, but not as a long-term solution to the enrollment increases.

Not only are officials looking for a place to build a new K-8 elementary school to accommodate the enrollment growth, they are simultaneously planning to expand capacity at the high school through renovation or new construction at the current site or another location.

And these projects are moving forward without any assistance from the state, which is already chipping in for the new Devotion School project.

No cost estimates are yet available, but town residents will eventually be asked to vote to raise property taxes to pay for the construction and potential land acquisition for the new elementary school and high school expansion. The current timeline has officials making a final decision on the elementary site by October, with a new elementary school opening in the fall of 2021.

Ellen Ishkanian can be reached at eishkanian@gmail.com.