The Wright Amendment, a 1979 federal law, limits most passenger service from Love to Texas and adjacent states. Kansas, Alabama and Mississippi were later added, and flights to Missouri were approved by Congress last year.
But the law still restricts Southwest, because it operates only at Love, from providing nonstop, one-stop or connecting service from North Texas to most of its largest markets, like Chicago, Phoenix and Florida.
Southwest, which is based in Dallas and dominates Love Field, refuses to operate at D/FW, where American is the dominant carrier.
Wright critics say the law crimps competition and keeps airfares high in North Texas. They argue that lifting the restrictions would lower fares from the region as Southwest and American compete for customers. Supporters of the law say a repeal would cause D/FW to lose passengers to Love and could hurt American and the area economy.
American executives have long been among the strongest defenders of the law, because it protects the airline's D/FW hub from competition at Love.
Some analysts say American has little to gain from any compromise on the Wright Amendment.
"American has no incentive whatsoever to support any kind of phaseout" of the law, said Scott Hamilton, an aviation consultant with Leeham Cos. of Sammamish, Wash. "It would be to their benefit to delay it as long as possible."
But the prospects of keeping the limits in place over the long term have dimmed over the past year. Although American still believes that a full repeal is unlikely soon, the company's executives are worried that other states could follow Missouri's lead and push to be exempted.
The airline will abide by a "cease-fire" on Wright-related lobbying until June 14, a deadline set by the city of Dallas. Southwest has also agreed to halt its lobbying until then.
If the issue is unresolved this year, the dynamic in Washington could change. Rep. John Mica, R-Fla., is campaigning to be chairman of the influential House Transportation and Infrastructure Committee. Mica is an outspoken Wright critic and could move a repeal bill through the committee.
"That would change the dynamic considerably," said Rep. Jeb Hensarling, R-Dallas, who is sponsoring a repeal bill.
American executives had previously expressed reservations about cooperating and said that sitting down with Southwest could raise antitrust issues.
But the sources familiar with American's strategy say the airline now believes that discussions that focus strictly on airport policy and possible legislation on the amendment would be allowed.
They plan to make their case to local officials that lifting the amendment is the wrong move for the community and that the best solution is to close the airport entirely.
That would force Southwest to move to D/FW, they will argue, and strengthen the larger airport while still fostering competition between the two airlines.
Southwest officials dismiss that idea. "It would be about a three-second conversation," Stewart said.
If closing Love isn't an option, American executives apparently feel there is some value in helping to shape any compromise. Chief among the airline's concerns are the size of Love and the scope of Southwest's operations.
The airport is capped at 32 gates under the Love Field Master Plan. Southwest operates 14 and holds leases on seven more. Continental Airlines has two gates, and American has three. Six gates, in the old Legend Airlines terminal, aren't under lease.
American executives would like to have as many gates as Southwest. If the size of the airport is unrestricted, that could mean building a new 21-gate terminal, the sources said.
"The model that American wouldn't like, but could accept, is a significantly larger Love Field with a lot of operations by American and other airlines," one of the sources said.
But the airline would prefer the airport stay at its current size or even shrink.
"Every additional gate [at Love] magnifies the problem," the source said. "Every fewer gate minimized the problem."
If Love is restricted, American would still want equal access to gates. That would mean Southwest would have to give up some of its gates to other airlines.
Dallas Love Field could see traffic double or even triple if the Wright Amendment were repealed.
A citizens committee representing neighborhoods around Dallas Love Field said it would withdraw support for the city's airport master plan if the Wright Amendment is repealed.
DFW Airport could support phasing out limits at Love Field only if the smaller airport closed as many as 14 of its 32 gates.
A consultant hired by Dallas-Fort Worth International Airport says an expansion of nearby Love Field would lead to reduced flights and millions fewer passengers each year at DFW.