The governor’s office is looking for empty office space to house the influx of migrants overwhelming the state’s shelter system, as first seen in Boston’s Seaport, where residents were surprised by potential plans for a Fort Point office building.

Many office building managers in Boston were contacted and the owner of 24 Farnsworth St., a private property, said that roughly 10,000 square feet of space was available for a potential overflow shelter, an official briefed by the Wu administration on the matter told the Herald Thursday.

Other cities in Massachusetts have been directed to do the same, the official said. An inquiry seeking confirmation from the governor’s office was not returned.

A spokesperson for the Universalist Unitarian Association, the owner per city records, indicated in a Thursday email that a migrant overflow shelter was being discussed as a “short-term use” for the Seaport building.

“Conversations are underway regarding a short-term use of the building that is in the public’s best interest and are in accordance with our values and principles as a faith tradition,” UUA public relations director Suzanne Morse wrote. “We have not yet finalized those plans.”

As first reported by the Herald, the city gave the Fort Point neighborhood a heads-up that the state was considering a safety-net site for migrants at that private office building, which caught some residents off-guard.

“The city will work with the state and other partners to ensure our residents have an opportunity to learn more and provide feedback regarding any proposed shelter sites, while prioritizing minimal disruption to area residents,” a Wu spokesperson said in a statement.

Thomas Ready of the Fort Point Neighborhood Association said he was alerted to the state’s potential plans at 24 Farnsworth St. by the city’s office of neighborhood services, as part of a partnership between the state and United Way — which was awarded a $5 million grant to fund safety-net sites for migrant families last fall.

His group provided neighborhood services with a list of questions that included concerns about the lack of bathroom and shower facilities that could accommodate a large number of people, and is pushing for a meeting with the city for answers.

He was surprised that a private building, rather than a city- or state-owned building was being considered for such a use. The community would have expected use of the Boston Convention Center instead, Ready said, pointing to its past hospital-related shelter use during the COVID-19 pandemic.

“It just caught us off guard,” Ready said, although he noted that the neighbors in his group seem to be “generally supportive” of the idea.

The revelation that the state is considering a Seaport office building for an overflow shelter comes on the heels of Mayor Michelle Wu stating that the safety-net site at the Roxbury Melnea A. Cass Recreational Complex is quickly reaching its 400-person capacity a week after opening.

As of Wednesday night, there were 327 people, or 95 families, at the Cass Center, which was targeted toward families sleeping overnight at Logan International Airport. The state and United Way have been evaluating additional safety-net sites, and “no new sites are confirmed at this time,” a Healey spokesperson said.

“If currently we’re housing the overflow of migrants at the rec center at Roxbury and it has been confirmed that we’re reaching capacity, then the city must be actively looking for other sites because we know we have more migrant families we need to house,” City Councilor-at-Large Erin Murphy told the Herald.

When asked whether a new safety-net site would be geared toward migrants arriving at Logan Airport, the Healey spokesperson noted that safety-net sites are for families who are on the waitlist for the state’s emergency shelter, which is capped out at more than 7,500 families.

“We estimate approximately half of the families are new arrivals,” Karissa Hand, the Healey spokesperson, said.

In an email obtained by the Herald, state Rep. David Biele said the potential safety-net site at the Fort Point building would be similar to one established in Newton by Catholic Charities, which received grant funding from United Way.

“United Way of Massachusetts Bay is working closely with the Executive Office of Housing and Livable Communities to identify sites to provide temporary safety-net shelter to eligible families with children and pregnant women and help set them on a path toward longer-term employment,” Brigid Boyd, a United Bay spokesperson said in a statement.

Eight safety-net sites accommodating a total of 97 families per night have been launched as a result of that grant program, Boyd said, noting that all are private properties.

A small site South of Boston will open soon, with more in the pipeline, Boyd said, adding that additional sites are also planned for Greater Boston, while declining to disclose locations for “security and privacy reasons.”

Murphy and City Councilor Ed Flynn have raised concerns about the lack of shower and bathroom facilities at the Fort Point site, which Flynn said should be a “non-starter.”