American Airlines was the first major carrier to charge a fee for checking one bag. United Airlines and US Airways followed.
Kellner said at an investor conference in New York that he is studying whether passengers prefer airlines that do not charge the fee, hinting his airline might go along if customers are not scared off by the extra charge.
"I also think there are operational impacts on a first-bag fee where you will have some delays," he said. "My general view is if those people need a product, how do we put that in an all-inclusive fare?"
Kellner noted that Continental Airlines Inc. still serves meals on its flights and includes the cost in the fare.
Bag fees are alluring to airlines that are looking everywhere for extra money to offset skyrocketing fuel costs. On Tuesday the Air Transport Association, said U.S. airlines could lose $13 billion this year as fuel prices outstrip fare increases.
Forecasts like that have renewed talk that big airlines could face bankruptcy by early next year unless fuel prices fall or fares rise sharply.
Continental executives said Wednesday they are focused on preserving cash. The Houston-based carrier has sold stock in Latin American airline operator Copa Holdings, extended a credit-card deal and refinanced debt to build cash.
Chief Financial Officer Jeff Misner said the company expects to end the second quarter with $3.2 billion to $3.3 billion in cash.
Like many other U.S. carriers, Continental plans to reduce the number of flights and mothball some planes later this year. That will save money by burning less fuel and paying fewer workers. Continental wants to cut 3,000 jobs. The airline also hopes that with fewer flights, it will have more power to raise fares.
Continental expects its U.S. capacity in the fourth quarter will be 11.4 percent less than a year earlier, roughly similar to cutbacks at Delta Air Lines Inc., American -- which is part of AMR Corp. -- and UAL Corp.'s United.
Continental shares fell 47 cents, or 3.4 percent, to $13.58 in midday trading.