NEW YORK (CNN/Money) - Some top officials at Delta Air Lines apparently now believe a bankruptcy filing there is inevitable, but the airline's chief executive said Thursday he still believes that a restructuring that does not involve a bankruptcy filing is the best route for the loss-plagued carrier.

"We continue to believe an out of court restructuring is the best way," Gerald Grinstein said in a conference call on second-quarter results, when asked whether a recent executive shake-up meant that a Chapter 11 filing -- which some analysts have said is inevitable for Delta -- was closer.

The Wall Street Journal reported Thursday that some top executives and board members are telling Grinstein that the turnaround plan implemented a year ago by the nation's No. 3 airline isn't working. And the paper also reports that the chance of bankruptcy could cause some top executives and pilots to leave in an effort to protect their pension benefits. That would cause the embattled carrier further problems.

The Journal reported that "bankruptcy proof" special pensions -- granted to top executives in 2002 to keep them at the carrier while it tried to reverse its losses -- could still be lost if there is a bankruptcy filing. That possibility, according to the paper, has stirred concern among top management that Delta (Research) could suffer an accelerated departure of key personnel.

Some senior pilots could be motivated to leave to secure lump-sum payments for which they are eligible under their pension program, according to the report. That creates the risk that Delta could see a shortage of certain categories of pilots, forcing the carrier to ground some aircraft.

Delta announced a management shuffle Wednesday, including a new chief financial officer and a new chief operating officer. Michael Palumbo left the company after only 14 months as CFO.

The Journal reported Palumbo did not have one of the special executive pensions, and that he and Grinstein had been staunchest among Delta management in their belief that bankruptcy could be avoided.

Delta posted a narrower second-quarter loss Thursday as it cut costs aggressively amid tough competition and high oil prices.

The company has not reported a quarterly profit since 2000. Analysts also expect losses to continue through at least 2007.

The continued reverses at Delta come at a time that some carriers have finally stemmed losses. American Airlines parent AMR Corp. (Research), the world's largest carrier, and Continental Airlines (Research), the nation's No. 4 airline, both ended long losing streaks Wednesday when they reported much better than expected earnings for the period.

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