The union says its board will meet with US Airways' top two executives next week.
CEO Thomas Horton met for three hours on Thursday with directors of the Allied Pilots Association.
Union spokesman Dennis Tajer said that Horton detailed his plan for American's parent company, AMR Corp., to emerge from bankruptcy protection on its own. He said the union invited US Airways CEO Doug Parker and President Scott Kirby to a meeting next week and the airline accepted. US Airways didn't comment immediately.
Tajer said the union board considered Horton's comments but still thinks a merger is better for pilots and the company.
American's pilots will own 13.5 percent of AMR after it emerges from bankruptcy under a contract that they ratified last week, and this week they joined the private merger talks between the two airlines.
Mike Trevino, a spokesman for American, said in an emailed statement that AMR used Thursday's meeting to thank union leaders for supporting the contract that pilots ratified. He said Horton and other company officials also went to "discuss the next steps in our evaluation of strategic alternatives and exchange information and thoughts about how to continue the positive momentum we are creating for our people and our customers."
American is the nation's third-biggest airline and US Airways is fifth-biggest. Combined they would be about the same size as industry leader United Airlines.
There is no guarantee that the current talks will produce a deal. Either airline could try to force a merger or acquisition of the other, or both could decide to remain independent.