NEW YORK (CNN/Money) - American Airlines parent AMR Corp.'s board of directors has voted to file for bankruptcy, perhaps as soon as Friday, unless it gets another eleventh-hour reprieve from one of its unions, according to another union at the troubled airline.

The AMR board announced Thursday evening that it had accepted the resignation of CEO Don Carty, who has become the focus of union outcry over executive compensation plans at the carrier. It did not mention anything about bankruptcy plans.

AMR Corp. CEO Don Carty resigned Thursday in an attempt to win union approval of concession deals.

But the Transport Workers Union, which represents most ground workers at American, said in a letter to its membership that the AMR board has voted to file for bankruptcy unless all three unions stand behind concessions agreed to last week before the controversy over executive compensation erupted. If the Association of Professional Flight Attendants doesn't drop its threat to have members vote again on the concessions they narrowly approved last week, the company will file for bankruptcy, TWU said.

Officials with the Allied Pilots Association told CNNfn Friday morning that they understood that flight attendants union had agreed to finalize the concession contract. But an official with APFA said any word of an agreement is "speculation" and would not comment further. A press conference had been scheduled for about 10 a.m. CT (11 a.m. ET) Friday by APFA, but an hour before it was due to start that press conference was in some doubt.

Shares of AMR (AMR: up $0.21 to $4.25, Research, Estimates) were trading lower in pre-market trading on bankruptcy fears, but they were about 5 percent higher in early trading Friday after reports of an agreement with the flight attendants union.

The TWU and the Allied Pilots Association agreed Thursday to sign off on the deals, with some modifications, including a shorter duration, that had been sought by the unions. But the Association of Professional Flight Attendants told its membership at the airline late Thursday that "at this time" it has yet to sign off on the agreement.

The APFA message said it would "continue to do everything possible to avoid a Chapter 11 bankruptcy filing by AMR. Discussions are ongoing at this time. The situation remains very fluid."

But that fluidity could come to an end soon. Reuters and the Wall Street Journal, quoting sources at the airline, said the filing could come as soon as Friday or as late as Monday.

The filing, under Chapter 11 of the federal bankruptcy code, probably would have only limited immediate impact on the airline's customers. In Chapter 11, a company is protected from creditors while it tries to reorganize and work out a plan to pay its debts.

American expects to fly a normal schedule for now and has said its frequent flier club members' miles are unaffected by the filing. But the bankruptcy could force the airline, which carries about one in five U.S. air travelers, to make deeper cuts in its schedule and route system in the long run.

The APFA's refusal to join the other unions in signing off on the modified concession pacts Thursday brought a thinly veiled attack from James Little, president of the Air Transport Division of TWU.

"We must do everything in our power to limit exposure of our contracts and our members in bankruptcy proceedings," Little's letter to members said. "Those who would do otherwise are clearly motivated by reasons other than the welfare of the members."

The three union deals save $1.6 billion a year in labor costs through across-the-board pay cuts and changes in work rules that allow for further staff reductions. One of the modifications agreed to in marathon meetings Wednesday between labor and management was to shorten the deals to five years from the previous six-year pacts.

American also made changes in nonunion employees' pay and staffing levels to bring total savings to $1.8 billion a year. It says it will need an additional $500 million in labor cost savings if it does file for bankruptcy to satisfy lenders who will fund operations during court-supervised reorganization. Those deeper cuts can be imposed by the bankruptcy court even if the unions or their membership refuse to agree.

Carty, 56, said he was resigning because it had become clear that "my continuing on as chairman and CEO of American Airlines is still a barrier that, if removed, could give improved relations -- and thus long-term success -- the best possible chance."

AMR named Carty's No. 2, Gerard Arpey, 44, as the new CEO. He had been president and chief operating officer since last year. It also named board member Edward Brennan as "executive chairman" of the board. An AMR board member since 1977, Brennan is the retired chairman and CEO of Sears Roebuck & Co.

Arpey said restoring trust with AMR employees would be a top priority in what he called "these extraordinary times.

"I will continue to lead by example," Arpey said. "Actions, of course, speak louder than words."  

-- CNNfn's Greg Clarkin contributed to this report.