HARTFORD, Conn. — A nonpartisan Connecticut think tank says there are ways to fix what seem like intractable budget deficits over the next two fiscal years, including turning over the operations of more state-run social service programs to the private sector.

In a new report to be released next week, the Connecticut Institute for the 21st Century estimates there is still room to save $1.2 billion over the next five years if the government contracts with private nonprofit agencies to provide services, such as group homes for people with developmental disabilities and mental health care.

It’s one of numerous money-saving ideas the nonpartisan institute says could save about $2 billion over five years. While some have been floated in the past with limited success, supporters hope there will be a greater support this year given the $2.3 billion state budget deficit projected in the fiscal year, beginning July 1 — a figure that has worsened in recent days.

The state’s main spending account is typically $18 billion.

“I think the timing is good,” Rep. Mary Mushinsky said of the new report’s release. The Wallingford Democrat has been trying to generate interest in the think tank’s research for the past several years. The report is being released as Democratic Gov. Dannel P. Malloy and legislative leaders are expected to begin budget negotiations in earnest next week.

All the leaders have repeatedly said Connecticut’s financial problems are so grave that “structural changes” are needed in how state government operates.

“As the state continues to grapple with its fiscal condition and the kind of easy things to do have been done, they have to look at more drastic, more fundamental changes in how services are delivered and how the state is organized,” said Bob Guenther, the institute’s executive director.

Some of the ideas are unpopular. For example, state employee unions have fought moves by Malloy’s administration to turn over control of social service programs to the private sector. Workers and parents of people with disabilities are pushing for legislation that would halt the privatization of some group homes and other Department of Developmental Disabilities services.

They claim clients will suffer in private-run programs where there’s high turnover rates, often due to low wages.

“Lawmakers should focus on real proposals like increasing the capital gains tax,” said Jennifer Schneider, a spokeswoman for the union SEIU 1199, adding how increasing revenue is the “only way” both private and public services can provide quality care.

Meanwhile, the Connecticut Community Nonprofit Alliance says turning over control of these social service programs to the less expensive nonprofits is the only way to ultimately protect services for the state’s most vulnerable residents.

“Essentially, if the state is paying more to serve a set of people than it needs to, then that’s making a decision to serve fewer people than we can,” said Gian Carl Casa, executive director of the alliance.

The Institute for the 21st Century also predicts up to $650 million can be saved between now and 2025 if Connecticut increases the number of people who receive long-term care in their homes rather than institutions. The organization also says an additional $300 million can be saved by 2020 if the state continues its efforts to reduce the prison population.

Various suggestions are made for cutting state pension costs, including increasing the retirement age for new hires. Also, there are numerous proposals to save money through technology upgrades and greater sharing and consolidation among city and town governments.

Republican Rep. Laura Devlin notes how some of the institute’s recommendations were included in past Republican budgets that didn’t pass. She said having a “third party, a nonpartisan group” endorse the same ideas could make them more palatable to budget negotiators in the coming weeks. This year’s legislative session ends June 7.