The state is not “currently” looking at the recently-closed Walgreens space in Roxbury as a potential overflow shelter for migrant families, the governor’s office said, debunking a rumor that had been percolating in some City Hall circles.

“The former Walgreens site is not currently under consideration,” Karissa Hand, a spokesperson for Gov. Maura Healey told the Herald.

When asked whether there was a contingency plan for when the overflow shelter at the Melnea A. Cass Recreational Complex reaches capacity at 400 migrants, many of whom are making their way there from Logan International Airport, the governor’s office didn’t get into specifics about what other sites could be used.

“We continue to evaluate other safety-net sites across the state,” Hand said.

The state-owned Cass Center, tapped last week to house migrant families with the state’s emergency shelter system capped at 7,500 families, is scheduled to close on May 31, per a commitment from the governor’s office.

The state is “working with communities small and large” to identify a new facility after it goes offline, Lt. Gov. Kim Driscoll said on a WCVB program Sunday.

Mayor Michelle Wu also doused the speculation, stating that the city was in talks with the property owner to preserve a pharmacy component to the space, in response to feedback from the community and criticism that followed Walgreens’ decision to close that location in a predominantly Black and brown neighborhood.

“There’s a very strong ask from the community that that was a key way that people could fulfill their prescriptions and get the medications that they needed,” Wu told reporters after an unrelated City Hall event Tuesday. “It would be great if we could identify a local business that could provide that service in that space.”

Wu said that pharmacy component could be realized through a local business, partnership between businesses, grocery store, or another venture. In the meantime, the city worked with Walgreens to transfer prescriptions to the chain’s Columbus Avenue store, and with Urban League to help pay for transportation.

“The city continues to try to use the connections, the leverage, the communications that we have with the property owner to keep those conversations going,” Wu said.

Her spokesperson added, “Various teams were involved in assessing every possible vacant building for the state’s timelines, but the focus on that Walgreens location has been ensuring there is a pharmacy and business in the space as quickly as possible.”

The property owner, listed as Four16 Warren Street Limited on the deed, made the former Walgreens space available for lease last month, according to Commercial Search, which lists it as a retail, medical office and industrial space.

“The available space has been occupied by Walgreens for 30 years, and will be available for the very first time” on March 1, the Commercial Search listing reads.

JP Plunkett, a broker with Red Dome Realty, said he was “bound by confidentiality” from revealing uses the property owner is considering for the space, “as is always the case in commercial real estate dealings,” but did say there was “lots of interest” from “various types of users.”

“The landlord is considering numerous users,” Plunkett told the Herald.