Lythgoe executive produced the show from 2002 to 2008, but then left to focus on international versions of So You Think You Can Dance, before coming back last year for the tenth season.
© Fox / Mathieu Young
© American Idol
There were prolonged negotiations lasting several months to get Lythgoe confirmed for season 12, E! News reports, with resulting delays in planning for 2013's show.
A source told the website that production is "way behind normal schedule" compared with previous years.
Lythgoe's immediate job once his negotiations are complete is to "lock in judges" to join recently-confirmed panellist Mariah Carey.
Rumoured potential judges have included Alanis Morissette, Nicki Minaj, Nick Jonas and Kanye West.
Meanwhile, Katy Perry is said to have rejected a $20 million (£12.6m) offer for the job and Miley Cyrus is reportedly out of the running.
