Matt Hancock has refused to rule out the possibility of running for the Conservative leadership in the future.
Appearing on the breakfast show, the health secretary said "the time hasn't come yet" to throw his hat in the ring.
"The time hasn't come for that yet. I'm concentrating, I am trying to deliver Brexit and of course I am running the NHS as well," he told talkRADIO's Julia Hartley-Brewer.
"There will come a time for that debate."
Casting his predictions for who will become the next party leader, the MP for West Suffolk said it was likely that the person who took over was somebody who "hasn't ever won a Tory leadership contest before".
"We have seen throughout history that the frontrunner doesn't win, hasn't ever won a Tory leadership contest before," Mr Hancock said.
"What matters is that we get a leader who is not just the leader for now, but is a leader for the future, and that is at the core of this."
So far, Esther McVey, Boris Johnson, Andrea Leadsom and Rory Stewart have all confirmed their leadership ambitions.
"It should be a contest about the future. Delivering Brexit obviously, then moving forward to all of the other things that matter," Mr Hancock continued.
"I want politics to be less divisive and more about bringing people together where they agree on something."