Mr Turnbull on Thursday rejected the suggestion made by Fairfax Radio Network morning host David Oldfield, saying he had a "hide".
"Can I just say, David Oldfield really has got a hide to make allegations like that without even giving me a call and giving me an opportunity to put across my side of the story," Mr Turnbull told the station this afternoon.
On Thursday morning, Mr Oldfield told listeners Mr Turnbull was looking to regain leadership of the Liberal Party from Mr Abbott.
He also commented that Mr Turnbull was pressuring independent MP Tony Windsor to support the government's carbon tax.
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Mr Turnbull said the subject which dominated his conversations with Tony Windsor was the government's National Broadband Network (NBN).
"So no, I haven't been talking to Tony Windsor about carbon taxes or emissions trading schemes or anything like that, but if he did want to discuss those with me I'd be happy to do so," he said.
"The suggestion that David Oldfield made that I was seeking to undermine Tony is absolutely untrue.
"There is no basis in fact - or the only basis for that is his fantasy - and it's really disgraceful.
"It's a reckless and disgraceful allegation," he said.
Mr Oldfield is not the only media commentator to suggest Mr Turnbull may want to take back the leadership of the coalition, or that he may support a carbon tax.
On Thursday morning, Macquarie Radio Network morning host Alan Jones said: "So unnamed Coalition carbon tax supporters have been expressing their support to Tony Windsor have they? I can imagine that perhaps Malcolm Turnbull has."
The leadership ambition suggestion has been raised in various newspaper opinion columns, without substantiation, at irregular intervals over past months.
