Dubbed "the New Dream Team" last fall, the trio have had a "fantastic" experience on the reality competition, says the source.
"They like and respect each other a lot. What you see on camera is exactly what you get when they're off – fun, playful but they all take this job very seriously."
FOX had no comment.
Host Ryan Seacrest said on Wednesday that auditions for season 14 start on June 18 and will hit up each of the judges' hometowns – New York, Nashville and New Orleans.
So Idol hopefuls you have been warned: Connick could spontaneously cradle you before Hollywood week.
With reporting by PATRICK GOMEZ