The four-piece became the first group to win "The X Factor U.K." in 2011 but ended their working relationship with Simon last year when they quit his Syco label.
Earlier this year, they announced their new show "Little Mix: The Search", which aims to put together the next big band - an idea music mogul Simon previously claimed was taken from him.
He has since moved the date for his "The X Factor: The Band" show forward to next month, and reportedly wasted no time in making a jibe about the girl band's new competition during the auditions for his show.
According to Britain's The Sun newspaper, he suggested one singer audition for the "Wings" hitmakers' show when he deemed them not good enough for his, quipping, "Little Mix are doing a show next year. You should apply. Tell them I sent you."
A source said about the jibe, "It was obviously a real dig at the girls' show. there is a proper feud."
Auditions for "Little Mix: The Search" are being held now, with the BBC show set to launch early 2020.