The Carter administration has agreed to give steel companies as many as three more years to meet clean air and water requirements if the industry will speed modernization of plants, according to industry and administrative sources.

The trade-off proposal follows meetings between leaders of the steel industry, the United Steelworkers of America and officials of the Environmental Protection Agency, seeking a new policy for the slumping industry.

President Carter said at his news conference yesterday that he expects to receive a "strong report" from the tripartite steel committee in a few days. t

Administration officials have been pressing to produce the report this fall in part as a response to Republican presidential nominee Ronald Reagan, who has pointed to the steel industry's plant closings and layoffs as an indictment of administration economic policies.

But the report has been delayed by negotiations between EPA and industry representatives, and industry sources were not willing to say yesterday that a final agreement has been reached.

A compromise appeared to be in hand last week, following meetings involving the three sides, headed by EPA administrator Douglas M. Costle, Steelworkers president Lloyd McBride and George A. Stinson, chairman of the National Steel Corp.

At issue now, sources said, is whether an EPA summary of those meetings reflects the views of the industry.

EPA's summary, dated Sept. 11, has not been released by the administration, and EPA officials refused to discuss it yesterday.

"All members agree that modernization of the steel industry is in the national interest," the report says. The industry estimates its modernization program will cost $4.7 billion a year, but it lacks the investment funds to reach that goal and also install the pollution control equipment required to meet existing environmental deadlines, the report says.

For these reasons, Congress should be asked to amend environmental legislation to give EPA the authority to grant limited postponements" of the clean air and water compliance deadlines.the report says.

The clean air compliance deadline is 1982, with 1984 for water pollution.

The report lists conditions that should be met before a company could qualify for a stretched-out deadline. The company's investment in modernized steel production must be accelerated; the company must meet environmental requirements at the end of the extended compliance timetable; and the quality of the environment in the area of the plant should not worsen in the meantime.

As a concession to the industry, EPA would agree to extend or "roll over" current EPA water discharge permits, which authorize steel companies to discharge waste water and pollutants into lakes and waterways.

Current water discharge permits for steel mills are due to expire before final EPA water pollution regulations can be issued, nullifying the industry's appeal for the use of less costly control equipment.

The report would extend discharge permits until the middle of next year, giving EPA more time to consider whether it will require advanced water pollution control technology, or settle for the best existing technology.

The political question facing the industry is whether to accept the environmental trade-off or to go forward with a lobbying campaign to persuade Congress to ease the environmental requirements and deadlines.

"We think the environmental problem has been oversold," said Fred Tucker, a vice president of National Steel, in a recent interview. "A much more rational approach has to be taken . . . We intend to get this message through to Congress," he said, through a "grass-roots" political action campaign next year.