The pair were both judges on the hit talent show's initial run, from 2004 to 2007, before "The Talk" host was replaced by British pop star Cheryl Cole. Sharon returned to the show for its 2013, 2016 and 2017 seasons - but was reportedly later fired for being "too old".
Speaking to Britain's Daily Mirror newspaper, the music mogul insisted he and Sharon are now on good terms, explaining: "I phoned her up the other day and said, 'Look, I'll be honest with you. How could I criticise you for being mouthy when it's the reason I hired you in the first place?!' "
"Sharon gets a bit carried away but deep down she's got real affection for the shows," he continued. "There will be other versions of these shows, I am sure, and she is always welcome back."
The star went on to call the mother-of-three one of his "good friends", and confessed: "If ever she had an issue, I'd be on a plane in five seconds. She'd do the same for me, I know that about her.
"There's absolutely no bad blood at all and like I said, when people think I'm annoyed with her, I'm not!"