Jacob Rees-Mogg has confirmed he "will not stand" for the Conservative leadership, after Theresa May vowed to step down if her withdrawal agreement gets the support of MPs.
Appearing on the breakfast show, the MP for North East Somerset joked that if he threw his "hat into the ring", it would be "thrown back" at him.
"My hat shall remain firmly on my head," he told talkRADIO's Julia Hartley-Brewer.
"I fear if I threw my hat into the ring it would be thrown back at me."
Breakfast show host Julia asked whether Rees-Mogg's 12-year-old son Peter, who recently accompanied him on a trip to Chequers, could do a good job as leader.
"He's not old enough, but I think he might do better than some people who are currently doing it," the politician said.
"He thought we should leave on March 29 at 11pm in the evening, along with most sensible Britons."
And when quizzed about how he would vote if there was a vote of no-confidence in the government, Rees-Mogg took aim at opposition leader, Jeremy Corbyn.
"I have more confidence in a government led by any Conservative leader than I do in one led by Jeremy Corbyn," he added.