About 55,000 city public- housing tenants are living in apartments far larger than they’re legally entitled to — and only a handful are cooperating with efforts to move them into smaller units, the head of the Housing Authority said yesterday.

“That’s a sizable number,” declared agency Chairman John Rhea at a hearing of the City Council’s Committee on Public Housing. “This is not a small issue.”

He warned that tenant hoarding of huge apartments “fundamentally jeopardizes” the operation of the nation’s largest public-housing agency and its 178,882 apartments.

The waiting list for city housing has 160,000 names.

And that doesn’t include the thousands of Housing Authority families crowded into apartments too small for them because turnover is so low for the largest units, which can be up to six bedrooms.

Councilwoman Rosie Mendez (D-Manhattan), the committee chair, said she knows of a family of three holding onto a six-bedroom apartment in her Lower East Side district.

Mendez said the family was once filled with kids who have since moved out, leaving a mother and her two adult children.

“They need to be moved to accommodate someone else who is in her situation [of years ago],” said Mendez.

“The number we didn’t get [at the hearing] is how many people are in crowded or severely crowded apartments,” she added. “It really is a problem.”

Officials said that more than 25,000 single tenants are occupying two-bedroom units, which require a minimum of three residents under federal guidelines.

Complicating matters is the fact that seniors are living in 30,000 of the 55,000 underutilized units and are generally reluctant to leave.

“This is leading to unbelievable anxiety,” Councilwoman Melissa Mark-Viverito (D-Manhattan) said.

Rhea agreed, but said his agency has no option in the matter because it stands to lose federal funding if the rules continue to be violated.

“Right-sizing apartments is a very delicate issue,” Rhea conceded. “Having said that, we have an obligation to act. The reality is we need compliance.”

He said the problem was “not aggressively handled” in prior administrations.

Officials said they are reaching out to seniors and their families and are looking to construct new buildings with studios and one-bedroom units to entice the entrenched to move.

There were 3,800 transfer requests in 2010 and 5,200 last year, leaving 48,000 tenants on the relocation roster.

“NYCHA expects these numbers to increase even more over the next year as every resident in under-utilized apartments is presented with their options,” the agency said.

Tenants get two chances to fill out a transfer request to the development of their choice. If they don’t respond, they’re placed on a waiting list for the first appropriate-size unit that becomes available in their borough.

Comments posted by angry tenants on the Internet indicate the Housing Authority is in for some fights.

“I’m all by myself in a two-bedroom app and I have lived here 26 years and I understand how people feel about families that needs apts but I’m not going to transfer from a community I’ve known my whole life . . . to move to bad neighborhood with a high crime rate and one day get shot,” a tenant identified as LinkCalderon wrote on the city-data.com forum site.

On the other side, JayBrown80 recommended gripers pipe down because they’re all receiving government subsidies.

“I totally support the safety net for those people who cannot help themselves,” he wrote. “But it’s a safety net, not a safety hammock where you get comfortable and stay there for the rest of your life.”