Clarkson clashed with Davis over her new album My December, when he expressed concerns that it would not be as commercially successful as 2004's Breakaway.
Cowell, who selected Kelly to appear on the first season of American Idol, has insisted that she should welcome any advice given to her by the 75-year-old record producer.
"Kiss and make up, decide what's best, get on with it! Clive Davis, at 80, is better than 99 per cent of the people in the music business in their 20s, 30s and 40s. And he's not 80, he's less than 80," Simon explained.
"Kelly is one of the best and she always will be, but Clive is the boss of the record company. It's his job to advise."