The move to at least partially privatize one of the nation’s largest water systems comes as the city considers unloading assets to finalize its debt-cutting plan, which is expected to be voted on by creditors this spring.

“We need infrastructure for water,” Detroit Emergency Manager Kevyn Orr said Monday at a panel discussion in New York hosted by the Manhattan Institute for Policy Research, a conservative think tank.

After a year in office, Mr. Orr has said an outright sale of Detroit’s water department, which serves nearly 40% of Michigan’s population, is unlikely. His preferred plan calls for leasing the water system to a new regional authority, which he said would bring in $47 million a year to the city for 40 years.

But suburban leaders so far have balked at their potential share of future costs for system improvements and unpaid water bills. It is still possible the city-owned system could continue to be run as a municipal department from Detroit, said a person familiar with the matter.

Privatizing water and sewer service in southeast Michigan could provide a test case for advocates who argue the private sector would bring greater efficiency and needed improvement to aging systems nationally. Opponents of such privatization efforts fear rate increases and question turning a public entity into a profit-making enterprise.

About 85% of all U.S. water agencies are public despite a swell toward greater privatization in the 1990s and 2000s. The city of Atlanta in a 1999 deal privatized its water system but reversed course after cost-cutting led to customer complaints.

“If Detroit does this, it will probably be the first really big public-private effort in the last 10 years,” said Peter Gleick, president of the Pacific Institute, a California environmental-research and advocacy group that studies water privatization and other issues.

The Detroit Water and Sewerage Department provides about 600 million gallons of water a day to Detroit and 127 suburban communities in seven counties. It has nearly $1 billion in annual revenue.

But like its city, the department has faced challenges. Until last year, it operated for decades under federal court oversight sparked by alleged violations under the Clean Water Act. A former department director pleaded guilty in 2012 to conspiracy as part of the corruption investigation into convicted ex-mayor Kwame Kilpatrick. Thousands of delinquent customers in Detroit who owe the department more than $100 million are being threatened with water shut-offs, according to city officials.

The city’s 21-page request for proposals sent Friday to prospective buyers described a department that collects more in revenue than it spends. But it faces five-year capital-improvement projects to replace water mains and upgrade treatment plants and pumping stations that are expected to cost $1.4 billion.

The system also had about $6 billion in debt as of March 15. In the event of a long-term lease or a sale, the city wants potential operators to come up with a way for the department to retire its debt if the transaction would cause the bond debt to lose tax-exempt status or end access to state financing. A potential operator also would have to wrestle with pension obligations for current and future department retirees, which the city estimates would require a payout of $675 million over 10 years.

In the request for proposals, Mr. Orr wrote that the city would “consider responses that contemplate alternative transaction structures, such as a long-term lease and concession arrangement or sale.”

The proposed privatization has some protection for ratepayers: An operator would have to cap rate increases at no more than 4% for the first 10 years.

Traditional city services are being outsourced across Detroit. A quasipublic authority and a private management company run the city’s convention center. Another authority is also taking over the city’s public lighting from a city department. Last month, Detroit’s City Council privatized trash service in a bid to improve service but without expected cost savings.

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Write to Matthew Dolan at matthew.dolan@wsj.com