American Airlines and US Airways will propose giving up some takeoff and landing rights at Reagan National Airport in Washington, D.C., in hope of settling a government lawsuit blocking their merger, two people familiar with the discussions said Wednesday.The offer could be rejected, and the airlines are still planning on the case going to trial Nov. 25, one of the people said. Both spoke on condition of anonymity because the talks are private. The Justice Department sued in August to block the merger, which would create the world’s biggest airline. The government says that the deal would restrict competition and raise prices, and that combining the airlines would make them too strong at Reagan National, where the airlines control 69 percent of the takeoff and landing rights, called slots, and hold a monopoly on 63 percent of nonstop routes. Reagan National is so busy that the government limits slots. It was not clear how many slots American and US Airways might propose to sell or lease to other airlines. The airlines’ proposal was first reported Wednesday by The Wall Street Journal on its website. Bloomberg News reported that attorneys for the two sides had opened exploratory settlement talks.Concessions at Reagan National have long been considered a key to any settlement. They would allow the Justice Department to say it had achieved more competition at the airport near downtown Washington. But government lawyers raised bigger concerns in their August lawsuit. They argued that the elimination of another airline — after four other mergers in eight years — would force consumers to pay more on hundreds of routes.In a statement Wednesday, US Airways Group said it still believes “there ought to be a realistic possibility of settlement” but declined to discuss specifics. A spokesman for Fort Worth-based American said the airline is open to a “reasonable settlement” but also declined to say anymore. The Justice Department declined to comment. Both sides agreed this week to use a mediator suggested by the judge who will hear the case in U.S. District Court in Washington. Six states remain party to the Justice Department suit, but Texas Attorney General Greg Abbott withdrew his opposition this month after the airlines pledged to retain air service to 22 Texas communities. Other airlines are watching the antitrust case closely. The CEO of Southwest Airlines said last week he was certain that Reagan National divestitures would be part of any settlement, and his airline would like to bid for the slots. The CEO of JetBlue Airways said last month that the merging airlines should give up some of their Reagan slots.