LOS ANGELES (Reuters) - The future of long-running animated television comedy "The Simpsons" appeared to be up in the air on Tuesday after 20th Century Fox Television said it could not continue to afford producing the show under its current business model.

Fox Television, a unit of News Corp, issued its statement after a report that the cast of the subversive comedy had refused a proposed 45 percent pay cut.

"We believe this brilliant series can and should continue, but we cannot produce future seasons under its current financial model," Fox said.

"We are hopeful that we can reach an agreement with the voice cast that allows 'The Simpsons' to go on entertaining audiences with original episodes for many years to come," the statement added.

"The Simpsons" is the longest-running comedy series on U.S. television and is currently in its 23rd season on Fox. The show also generates billions of dollars through global syndication, as well as DVD and merchandise sales.

The Fox statement followed a report on news website The Daily Beast that the six principal voice cast members -- including the voices for Homer (Dan Castellaneta), Marge (Julie Kavner), Bart (Nancy Cartwright) and Lisa (Yeardley Smith) -- were having difficulty negotiating their contracts that currently see them earning around $8 million each per season.

The Daily Beast, quoting an unnamed insider, said Fox had threatened to end the series if the cast refused to accept a 45 percent pay cut.

The Daily Beast also said the cast had tried unsuccessfully to negotiate a 30 percent pay cut in return for a portion of the show's profits.

Fox declined to comment further.

"The Simpsons" is broadcast in more than 100 countries and 50 languages and has become a staple of American culture, with the family earning a star on the Hollywood Walk of Fame.

(Reporting by Piya Sinha-Roy; Editing by Jill Serjeant)