Australia's most wanted dogs are set to fly out of the country in their own private jet.

Agriculture Minister Barnaby Joyce said he was elated Johnny Depp's terriers, Boo and Pistol, would be soon be departing the country, calling it, "the best news I've got".

"I'm informed that Pistol and Boo are preparing to fly on a private jet back to the United States, which is the best news that I've got," Mr Joyce told ABC NewsRadio.

"Obviously there's an investigation as to how they came out into Australia.

"Mr Depp decided that he'd step around our nation's laws."

The Daily Telegraph reported that Depp and his wife Amber Heard have told the Department of Agriculture they will fly out with Pistol and Boo this evening.

Mr Joyce said the fact the dogs were not declared to Customs was a "concern" for Australia "because Pistol and Boo come from a country that has rabies".

"Pistol and Boo have had their lives threatened by the actions of Mr Depp," as a consequence, Mr Joyce added.

Depp is on Queensland's Gold Coast to film the latest instalment of the Pirates of the Caribbean franchise.

He faces a formal interview with quarantine officers as part of investigations into how the Yorkshire terriers were allegedly smuggled in.

Mr Joyce said this was not the first time high-profile foreigners had brought animals into Australia without authorisation — and that in the past the animals had been put down.

"We've had other dignitaries who've brought in, for instance, in bullfrogs...to eat. We had to euthanase them," he said.

"Obviously my preference is not to destroy these two dogs."

Mr Joyce's department later released a statement which read: "Prior to the dogs' departure, the Department of Agriculture will issue an export certificate and correspondence detailing the circumstances surrounding their entry into Australia to help facilitate access to the United States.

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"Given that Australia is considered to be free of rabies and that the United States has different certification requirements to us, we don't anticipate that the dogs will have any issues re-entering the United States.

"The Australian Government takes biosecurity extremely seriously. We have a world-leading biosecurity system that protects Australia's human, animal and plant health from exotic pests and diseases.

"It is critical that we maintain our unique pest and disease free status and we appreciate Mr Depp's cooperation in resolving this issue."

Joyce under fire from Palmer, Sandilands

Meanwhile, Federal MP and businessman Clive Palmer has hit out at Mr Joyce on Twitter, saying Australia's reputation and film industry will be adversely affected if the Yorkshire terriers are put down.

Mr Palmer posted tweets this morning saying the simple solution was "to put #deppsdogs into quarantine", in response to Mr Joyce's comments to the media about the dogs.

Mr Palmer tweeted: "#PistolandBoo shouldn't have their lives threatened. The simple solution is to quarantine them #deppsdogs."

Mr Palmer also said Mr Joyce's actions were "... a waste of time and will result in a bad reputation for Australia and will hurt the struggling film industry on the Gold Coast".

"@Barnaby_Joyce is making Australia the laughing stock of the world. Simple solution would be to put #deppsdogs into quarantine today," the Palmer United Party leader tweeted.

Mr Palmer went as far as tweeting Mr Joyce "will costs Australia a thousand jobs and millions $$ in exports".

"You sound like an absolute clown telling the guy to bugger off back to Hollywood or we'll kill his dogs. You sound like an idiot," Sandilands said.

"You're a government minister, not some idiot off the street mouthing off to a news camera. Have some decency."

Mr Joyce fired back, saying: "Jeez Kyle, that seems interesting coming from you mate.

"You're a savage little man, aren't you?"

The Australian Government said it had supported the makers of Pirates of the Caribbean.

It allowed two capuchin monkeys to be brought into the country for filming, but those animals did go through proper quarantine processes.