Holiday Inns Inc. is selling its Delta Steamship Co. subsidiary in a complicated transaction in which the Federal government is expected to provide the buyer with $575 million to rebuild Delta's aging fleet.

The buyer, Crowley Maritime Corp. of San Francisco, a tug and barge operator, has made the Department of Transportation's Maritime Administration an offer it is not expected to refuse: in exchange for the $575 million, paid over six years, Crowley will give up Delta's long-term Federal subsidy contracts, which Crowley says would cost the government more in the long run.

Crowley would use the money to order five large, efficient container ships from foreign shipyards, and put them into service on routes to South America and Africa now served by Delta's mostly-obsolete fleet of 24 vessels. Crowley expects the Maritime Administration to approve the deal because it fits in with the Reagan administration's policy to reduce long-term subsidy commitments and to encourage American ship companies to rebuild their fleets by acquiring new vessels at low-cost foreign yards.

Crowley originally asked for $762 million. The new figure, $575 million, was reached after extensive negotiations between Crowley and the Maritime Administration, and represents Crowley's "bottom line," according to Mark P. Schlefer, Crowley's Washington attorney. "If they don't accept this, they don't have a deal," he said.

Delta, based in New Orleans, is one of eight American ship companies that receive Federal subsidies to help them stay competitive with lower-cost, more efficient, foreign vessels. Last year Delta's operating subsidy was $58 million, a figure that can be expected to rise each year as wage rates and fuel and repair costs go up.

The Maritime Administration's contracts with Delta obligate the government to keep paying this ever-rising subsidy into the mid-1990s. Schlefer said the arrangement offered by Crowley would cut the obligation off after six years, and would cost the government no more than it would have had to lay out anyway under the existing subsidy contracts. Crowley will keep Delta's present management, he said, and "honor all existing labor contracts."

A spokesman for the Maritime Administration said no decision has been made on the Crowley offer. Earlier this year, however, MARAD approved a similar, more costly, arrangement with United States Lines, and there is no indication that its response to Crowley will be different. Other maritime industry officials said they expect the Delta transaction to be approved, based on the administration's policy and the U.S. Lines agreement.

For Holiday Inns, the sale of Delta puts an end to an ill-fated diversification program that took the company far afield from its original hotel business. Holiday Inns acquired both Delta and the Trailways bus system when it bought TCO industries in 1969. Trailways was sold in 1979, and Holiday Inns has said it intends to concentrate on its lodging, food and gaming operations.

The sale to Crowley will bring in only $96 million, which maritime industry sources said is about $50 million less than Holiday Inns originally asked.

Delta accounted for about 23 percent of Holiday Inn's total revenue last year and accounted for $46.2 million of a pretax profit of $290.8 million.