The long-running animated series could be axed due to a contract dispute between the show's voice actors and 20th Century Fox.
However, some of the show's producers have now agreed to a reduced wage in order to extend the series beyond its current 23rd season, according to Entertainment Weekly.
20th Century Fox TV previously demanded that the show's voice cast take a 45% pay cut, and later rejected a counter offer of a 30% reduction, plus a portion of the show's back-end earnings.
However, all sides are said to be committed to reaching a deal, with at least one final season of The Simpsons likely to be produced.
The Simpsons first premiered in December 1989. It is the longest-running American sitcom, the longest-running American animated programme and the longest-running American primetime scripted television series ever.
The show returns to Fox at 8/7c on October 16.
> Simpsons execs tease guest stars, 500th episode, final season at Comic-Con<
Watch a clip from The Simpsons below: