The 44-year-old singer, who has been on the show since 2011, is negotiating a spot for series 13 after sitting out last season, reported People magazine.
"J Lo is very close to signing a deal with Fox to return to 'American Idol 'next season. Both Fox and Jennifer are very happy about this and want it to happen very much," a source said.
"Most of what you've been reporting is true ... Jennifer has been a close part of the show all along. There is no deal with her or with anybody else," Kevin Reilly, FOX's entertainment chief, said.
While Mariah Carey, Nicki Minaj and longtime judge Randy Jackson have quit the show, Keith Urban has signed on for another year.
"Keith is going to return to the show. Keith did a great job last year. Keith's a really funny guy - I don't think he got to let his personality shine through," Reilly added.