"She's met with [Idol] producer-creator Simon Fuller several times," an insider told Life & Style in a Wednesday report.
"They like her -- she's a good fit -- and she likes it. Now it's just a question of how to fit her in."
However, producers are denying that Simpson would be the next Cowell.
"She's not his replacement -- they're two entirely different personalities," the insider said.
Instead, Simpson would join American Idol as part of a huge shakeup that could include an entirely new judging panel.
"This is part of a massive overhaul of the show. There may be more judges, more opinions," the insider told Life & Style.
Rumors that American Idol may be replacing its entire judging panel have surged since multiple reports that former American Idol producer Nigel Lythgoe -- who left the show in 2008 to focus on So You Think You Can Dance -- is near a deal to return to the show surfaced on Monday.
Earlier this year, Lythgoe repeatedly told reporters he would address Cowell's exit by replacing Idol's entire judging panel if he were still in charge of the show.
"I'd lose the fourth judge, I don't like four judges. I'd keep Ryan Seacrest and probably change the whole panel to go with [Elton John]," Lythgoe told the New York Post in March.
"I would replace the entire judging panel," he elaborated to Zap2it in April. "I don't think it really works replacing one person. They don't have a great deal of chemistry at the moment. Ryan and Simon have fallen out. It's uncomfortable to watch. [Ellen DeGeneres] hasn't worked out as well as we would have hoped."