Both reality singing shows air on Fox, and Cowell praised Idol showrunners for the decision in a tweet on Monday evening. However, the news has not yet been officially confirmed by the network.
"Just heard randy is back on idol. Right decision," Cowell wrote, but did not elaborate on where he had heard the news.
Jackson himself addressed rumors that he might be leaving American Idol in an interview earlier on Monday, saying that people should not "believe everything they hear".
Mariah Carey will join the American Idol judging panel for the show's next season, and is currently the only judge who has been officially confirmed for next year.
American Idol is expected to return to Fox in January 2013.