Clive Lewis said it would be "foolish to say never" to the possibility, but that he backed Jeremy Corbyn.
Mr Lewis said he was "75% hopeful" Mr Corbyn could lead Labour to victory at the next general election.
And he said he was "greatly" annoyed by "mischievous" speculation about his leadership ambitions.
Speaking on BBC Radio 5 live's Pienaar's Politics, the Norwich South MP - who quit the shadow cabinet last month rather than vote in favour of the government's Brexit bill - said it was "flattering" to be "touted as a future leader".
It was "possible" that some figures close to Mr Corbyn could be behind the speculation, he said.
Pressed on whether he wanted to ever lead Labour, he said: "Never say never, I will say that. But at this moment in time we have a twice democratically elected leader, Jeremy Corbyn.
"I'm still supportive of Jeremy Corbyn. I will be doing all I can along with the rest of my colleagues in the Labour Party to varying degrees to make sure that he becomes the next prime minister of this country.
"There is no ifs, no buts. That's where I am."
Asked how confident he was on a scale of one to 100 that Mr Corbyn could lead Labour to a general election victory in 2020, he replied: "I would say I'm 75% hopeful it can happen.
"Given ... the situation we find ourselves with Brexit - the chaotic situation - it's constantly moving. It would be a challenge for any leader I think."
The Labour leadership came in for renewed criticism after the party lost the seat of Copeland to the Conservatives in last month's by-election.
It was the first by-election gain by a governing party since 1982.
Speaking on the BBC's Andrew Marr show, shadow chancellor John McDonnell said Mr Corbyn would lead Labour into the 2020 general election.
"Of course we are building up a succession for the long term future and we have got some really great young talent coming through but they need more experience before eventually they will succeed," he added.
Mr McDonnell also categorically ruled himself out of a future run for the leadership.
Asked about his claim of a "soft coup" against Mr Corbyn, he said a "number of people" within the party had been "stirring" ahead of the by-elections in Copeland and Stoke Central.
But he said he planned to "have a cup of tea" with arch critic Lord Mandelson.
"There will be lots of things we agree upon. There will be some disagreements. But I think the most important thing that we have got is a responsibility to our party but more importantly to the country," he said.
A Labour MP who quit the frontbench to rebel over Brexit says he will "keep the option open" of one day running for leader.