Outgoing Deputy Mayor Alicia Glen touted City Hall’s new effort to save the city’s embattled Housing Authority by privatizing the management of nearly a third of its 175,000 units.

“The future of public housing in NYC is going to be that a lot of those units that have been managed by the housing authority really need to be converted into Section 8 housing projects and run by other people,” Glen told real estate publication The Real Deal. “That’s something that took a while to get into the ether and get socialized and accepted.”

She added: “But now it’s gaining a lot of momentum.”

City Hall hopes that the private management effort will fund roughly $13 billion of NYCHA’s enormous $32 billion bill to bring its 325 complexes back to a state of good repair.

The Housing Authority is the biggest landlord in the city — providing housing to more than 400,000 New Yorkers — and is under the gun of a possible federal takeover after years of mismanagement and a series of scandals that have shredded its one-time image of competence.

Federal regulators set a Jan. 31 deadline for complex negotiations among City Hall, the federal Department of Housing and Urban Development and federal prosecutors in Manhattan over NYCHA’s future in December — warning that failure to reach a deal could result in a federal takeover.

However, the government shutdown has put those talks on ice as most of HUD’s staff and much of the civil case staff in the Manhattan federal prosecutor’s office is on furlough.

Glen, who has overseen housing and economic development for the de Blasio administration, is stepping down in March.