SAN JOSE — Facing a growing homeless population that is among the highest in the United States, San Jose is ready to try a new strategy to get people off the streets: pay to put some of them up in local hotels and motels, potentially for years.

City Council members on Monday will discuss the proposal — a first for San Jose — that has been gaining steam at City Hall for the past year as housing prices continue to climb and landlords become pickier about renters. The problem has gotten so bad that about 100 homeless people roaming San Jose streets have publicly funded vouchers for subsidized housing but cannot find a place that will accept them.

Unlike the revolving-door atmosphere of shelters, the latest plan would give homeless people a room for up to five years while a nonprofit would provide services such as job hunting and permanent home searches.

“It’s just a tough place to live because of how expensive it is,” said Leslye Corsiglia, the city’s housing director, who called it an opportunity for homeless people “to get themselves settled and together so they can move into other housing.”

While the exact number of people who would receive rooms is dependent on available funding and willing motel and hotel owners, only a fraction of the city’s 4,770 homeless would be helped. Officials haven’t decided whether the chronically or the newly homeless would get priority.

The city figures it would cost $1 million a year to house 60 people, including initial costs to spruce up the rooms. San Jose has $3 million to spend on homeless services this year, while Santa Clara County, which would help fund the program, has more than $8 million available.

Meanwhile, many of the city’s rooms are located at luxury hotels or economy chains that aren’t interested in the deal.

For some down-on-their-luck motel owners, however, the proposal would result in welcome business. They would lease as much as 49 percent of their rooms to a yet-to-be-determined nonprofit that would rent the rooms to homeless people who would pay using federal Section 8 housing vouchers or city “coupons.”

“I love this idea, I have no objection to that at all,” said Sanjay Patel, who owns the 40-room City Center Motel on the southern edge of downtown and has been struggling to find customers. “I’d rather have full than empty.”

Patel said he couldn’t get anyone to stay there at $80 to $90 a night. So he’s been booking rooms to long-term guests — mostly San Jose State students and cooks at nearby restaurants — who pay a discounted rate of $25 per day. The homeless also likely would pay a lower rate, estimated to be about $40 a day, but the money at least would provide long-term stability for motel owners.

San Jose’s homeless population has grown 16 percent in the past year, and about three-fourths of those residents spend most nights sleeping outside, a biannual homeless count last year concluded. Three people died of exposure in the city during a December cold snap.

A recent federal report found Santa Clara County’s homeless population, which totals 7,631, was fifth in the nation behind only New York City, Los Angeles, Seattle and San Diego.

At the same time, the fair market rent for a San Jose studio apartment is $1,079 a month, among the highest in the nation, while a full-time minimum wage job pays $1,600 a month before taxes. Two-thirds of San Jose’s homeless said in a recent survey that their biggest barrier to housing was the high rents.

A motel room at a discounted nightly rate wouldn’t be inexpensive — perhaps more than $1,000 a month — but with a nonprofit acting as the landlord, it would ensure that homeless who receive rent subsidies aren’t turned away. Voucher recipients must pay as much as 35 percent of their income on rent, while the subsidy covers the rest — typically up to about $850 for single-occupancy units.

“It’s not going to completely solve the housing crisis, but it’s important to do all of these things because they all add up,” said Jenny Niklaus, CEO of EHC LifeBuilders, one of the county’s largest homeless shelters and services providers. She is particularly encouraged because the long-term housing security “stabilizes people so they can address the other things in their lives.”

San Jose wouldn’t be the first city to move the homeless into long-term housing. In San Francisco, the city oversees a similar program in which homeless people can live in single-room occupancy hotels.

The full City Council could pass the legislation this summer, and the program could start soon after. First, council members on the Community and Economic Development Committee appear primed to give the plan a thumbs-up Monday.

“We’re a caring community,” said Councilwoman Rose Herrera, who heads the committee and supports the plan. “This gives us some immediate ability to put people into housing. We can help them get back to where they should be.”

Follow Mike Rosenberg at Twitter.com/rosenbergmerc.