"There has been nobody that has been looking to appear to be his successor or to be his replacement," he told a Politics in the Pub session on the NSW north coast.
But when asked what he thought would happen next Tuesday, he said: "We'll see. You'll just have to wait and see."
Mr Turnbull has denied canvassing support for a tilt at the top job, as has his colleague Foreign Minister Julie Bishop.
However, this might not preclude them running if Mr Abbott's position is declared open.
Mr Abbott doesn't expect any spill motion to go ahead and has ruled out facilitating such a ballot, saying it would be a "distraction".
"I don't expect anything like that to happen because I know that this is cabinet working together for the good of our country," he said last night.
The prime minister is confident of remaining leader and says he trusts Mr Turnbull and Ms Bishop.
As of yesterday, Mr Abbott's backers were estimating there were only 10 to 15 coalition supporters for a change, while others suggested the figure could be 30 out of a 102-strong party room.
Mr Pyne said this week - which has been dominated by potential threats to Mr Abbott's position - had been one the government would rather not repeat.
"We can't have too many weeks like this or we will blow the opportunity that the Australian people have given us to help make their lives easier," he said.
His position as Leader of the House meant it was his job to find out what his colleagues were thinking.
"And I have been talking to my colleagues and there are obviously some people who are saying that there should be a vote on Tuesday because they said it publicly and they have said it privately," he added.
Asked if he believed Mr Abbott had the numbers, Mr Pyne said the parliamentary party knew the worst thing it could do was change the leadership.
"We have to support the prime minister," he said.
"I will certainly be supporting him if there is any kind of ballot on Tuesday, but I can't speak for all of my colleagues in a secret ballot."
Mr Pyne also played down a Fairfax Media report on Friday that Mr Turnbull was "underwhelmed" by the response he got from the prime minister during a private one-on-one meeting last week on the leadership issue.
"There wasn't a secret meeting between Malcolm Turnbull and the prime minister," Mr Pyne said.
"All the cabinet were in Canberra last week for two days of meetings and we all had meetings with the prime minister of one kind or another.
"Malcolm had a regular meeting with the prime minister."
- AAP
