Officials from the two companies declined to comment, but The Wall Street Journal reported that their boards are scheduled to meet separately on Wednesday, and a deal could be disclosed by Thursday.
"Discussions are still ongoing but no decision has been made," a person familiar with the talks told AFP.
A merger would assemble a powerful fleet of about 1,530 mainline and regional aircraft flying some 6,428 daily flights. Combined revenues of $38.7 billion in 2012 would put them slightly ahead of United and Delta Airlines.
The deal would help complete American's expected emergence from bankruptcy restructuring.
It would also cap a round of big airline deals that has remade the US airline business into a handful of giant carriers like Delta and United, which acquired Northwest Airlines and Continental respectively.
The idea of an American-US Airways tieup has been floated since American went into bankruptcy protection in November 2011.
The carrier has continued to operate under court supervision even as it sought to slash costs by renegotiating wage and benefit deals with its unions.
The prospect of a merger strengthened when union leaders publicly endorsed it in April, and talks moved ahead when the two firms signed a non-disclosure agreement to exchange confidential information in August.
"It's probably beyond the point of no return" said John Thomas, head of the global aviation practice at L.E.K. Consulting.
The move would allow deeper savings than either firm could achieve on its own, Thomas said. The firms could, for example, route more customers onto larger planes, which is more efficient for carriers.
There is little overlap in the route networks of the two airlines. The combined company would increase American's offerings in the Northeast and in the southwestern city of Phoenix, where US Airways has hubs and is strongest.
News reports say the combination could bring some $1.2 billion in cost savings.
Overall, the US industry is in better shape than a few years ago, with higher fares and fewer empty seats as the US economy rebounds.
Thomas said airlines have also picked up an additional $8 billion a year from charges on bag checks, food and other items.
A deal would require not only the customary approval of regulators and shareholders, but also the support of the US Bankruptcy Court that has been overseeing American's Chapter 11 bankruptcy process.
Thomas said the combined firm might be required by antitrust regulators to divest some routes where there is overlap.
Outstanding issues include what role American chief executive Tom Horton would play in the new company. US Airways CEO Doug Parker is expected to lead the new company.
Tom Hoban, the communications chairman of the Allied Pilots Association union group, said American's labor groups support the merger because it offers "better terms" to workers than what would come from a free-standing American.
"It's got a momentum of its own," Hoban said of a deal. "Labor is strongly behind this merger. The investment banks are supportive. American's senior executives are reluctant latecomers."