Tory MP Johnny Mercer has suggested he does not aspire to lead the party.
The former Army captain also said the Conservatives must honour their commitments to defence spending, amid reports that plans are being blocked by the Treasury.
Backbencher Mr Mercer is seen as a rising star in the Tory ranks, having been elected to his Plymouth Moor View seat in 2015.
Appearing on Sunday with Paterson on Sky News, Mr Mercer was asked whether he aspired to lead.
He immediately replied "no", adding: "I've got a very busy seat down in Plymouth and I like getting on with that."
He had earlier said Theresa May was a good Prime Minister, adding: "We need to get on and deliver Brexit, that is what people want on the doors in places like Plymouth.
"We need to deliver that, and then get on to what being in the Conservative Party actually means beyond that."
The Tory manifesto vowed to meet Britain's Nato commitment to spend at least 2% of GDP on the Armed Forces and also to increase the budget by half a per cent above inflation each year.
But reports in The Telegraph suggest the move is being blocked by Treasury officials, who say the Conservatives' election failure means they are no longer bound by a manifesto pledge.
Mr Mercer told Sky he expected his party to honour the commitment, which he had raised with Defence Secretary Sir Michael Fallon last week.
"People voted for a Conservative Government, and part of that was a 0.5% increase above inflation," Mr Mercer said.
"We need to see that, because I think the defence spending is too low.
"I think if you look at both the threats we're currently facing, which by Michael's own admission have developed significantly in the last few years, and Brexit, what the UK looks like after Brexit, there is an increased role for our Armed Forces and we've got to fund it."