The business secretary said on Sunday that Conservative MPs needed to “stop messing around” and support Sunak.
But asked if she still had future leadership ambitions, Badenoch said: “You never really know these things until you’re in the moment.”
With the Conservatives trailing 20-points in the polls, there have been reports of fresh moves to trigger yet another leadership contest and get rid of Sunak.
Badenoch, who is a favourite of grassroots Tory members and stood in the contest that saw Liz Truss elected PM, has been named as a possible replacement.
She then backed Sunak in the contest that followed Truss’ short time in No.10.
According to the Sun on Sunday, some Tory rebels want to install Badenoch as leader and see her as the “the next Mrs Thatcher”.
But speaking to Sky News on Sunday morning, she professed loyalty to the prime minister.
“I fully support he prime minister. They need to stop messing around and get behind the leader,” she said.
“The people who keep putting my name in there are not my friends. They don’t care about me, they don’t care about my family or what this would entail. They are just stirring.”
Badenoch added; “We can’t just keep treating prime minister’s as if they are disposable.
“People like me in the cabinet, MPs and quite frankly all politicians and the country want to see him survive and do well, we want to see him succeed.”
In a separate interview with the BBC’s Sunday with Laura Kuenssberg programme, Badenoch “absolutely” denied she had discussion with rebel MPs.
But asked if she would want to be leader in the future, Badenoch said: “I did in July 2022, I did stand and I lost.
“If you’d asked me two years ago in January 2022 I would have laughed it off and said it was completely crazy idea. You never really know these things until you’re in the moment.”
Last week former cabinet minister Simon Clarke called for Sunak to be ousted as Tory leader as the party was set to be “massacred” at the ballot box.
His intervention was met with a fierce backlash from other Tory MPs, including former home secretary Priti Patel who slammed it as “facile and divisive self indulgence”.
But according to The Times, a rebel group of around ten Tory MPs were working together from a base in central London in the hope of installing a new party leader.
Upcoming by-elections in Wellingborough and Kingswood are not expected to go well for the Conservatives, with May’s local elections across England and Wales also set to be a bloodbath for the party.