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He resigned his position as home affairs minister after narrowly losing a leadership challenge to Mr Turnbull on Tuesday.
But Mr Dutton says he is preparing for another challenge.
"You don't go into a ballot believing that you can lose, and if I believe that a majority of colleagues support me then I would consider my position," Mr Dutton told 3AW radio in Melbourne on Wednesday.
"I'm speaking to colleagues. I'm not going to beat around the bush."
Mr Dutton also wants a royal commission into energy and fuel prices if he becomes leader.
"There's something that's not right, there's something that stinks about some of these electricity companies and fuel companies," he said.
Mr Dutton said immigration needs to be pushed towards Western Australia, South Australia and regional areas to reduce congestion in major cities.
He also said the government's company tax cuts were not going to get through the Senate, so the money should be spent on education and health.
The 47-year-old said on Tuesday he was going to the backbench to give him a chance to "smile" a bit more.
"When you're stuck in front of a camera talking about the serious issues of national security and border protection, it's pretty hard to crack a smile," he said.
However, Mr Dutton failed the AC/DC test on Triple M radio by not being able to name his favourite of the great Australian band's songs.
"Ah, I've had about an hour-and-a-half sleep last night. I haven't sorry. That'll be the gotcha of the day," he conceded.
Triple M played Dirty Deeds Done Dirt Cheap for him later.