Australia’s deputy prime minister, Barnaby Joyce, has said the government will examine whether Johnny Depp committed “perjury” by smuggling dogs into the country while knowing it was illegal.

The saga of Pistol and Boo, the Yorkshire terriers who infamously landed the then Hollywood couple in strife in 2015, took another twist with allegations by Depp’s former managers that he was “fully aware that he was illegally bringing his dogs to Australia”.

However, legal sources immediately poured cold water on Joyce’s suggestion, telling the Guardian that Depp could not be charged with perjury when he made no representations in the Australian court case.

Depp’s former wife Amber Heard paid a $1,000 fine last year after pleading guilty to making a false customs declaration that she had no animals, in what a Gold Coast magistrate accepted was a paperwork bungle involving a disgruntled Depp staffer.

But in legal filings in a US dispute with Depp, the Management Group (TMG) alleged Depp “falsely claimed to authorities and in public press interviews that the incident was a big misunderstanding because he supposedly believed his staff had obtained the necessary paperwork”.

When confronted by Australian authorities, Depp “pressured one of his long-term employees to ‘take the fall’”, TMG alleged in papers obtained by People.

Joyce, who publicly traded barbs with Depp after threatening to have the dogs killed unless they were returned to the US, said the government would “have a look” at whether it could take further legal action in response to the fresh allegations.

“If the allegation is correct, there is a word for that – it is called perjury,” Joyce told ABC on Tuesday. “That is another question that, if that was true, Mr Depp would have to answer for.

“It doesn’t matter if you think that you’re Mr Who’s Who of Hollywood, you’re going to obey our laws.”

Joyce separately told News Corp, “If the allegations that have been made against him are correct, and I’m not saying if they are or aren’t, then that would be perjury.”

However, sources including a commonwealth lawyer said if Depp had made no sworn statements in the case, that ruled out a perjury charge.

The relevant law, section 43 of the Crimes Act, makes it an offence if “the person attempts to obstruct, to prevent, to pervert or to defeat the course of justice in relation to a judicial power”.

Depp accompanied Heard to the court and appeared in a widely lambasted “hostage video” apology that was played before the magistrate but gave no sworn evidence.

Michael Cope, a prominent Brisbane solicitor, said: “It wouldn’t be perjury.”

“He didn’t get charged at all and if he’s not said anything to anybody, either in a courtroom or filling in a form where he’s provided a statutory declaration, or similar document, then I don’t see where he’s committed any offence.

“And she’s pleaded guilty to the offence that’s been committed. So what’s the point then?”

Heard originally faced criminal charges of illegally importing animals, which carried a maximum penalty of 10 years jail, but these were dismissed by the Gold Coast magistrate Bernadette Callaghan.

Heard had six months earlier offered to plead to the false customs declaration in exchange for the dropping of the more serious charges but commonwealth prosecutors, acting on instruction from Joyce’s agriculture department, rejected the offer.

Depp once referred to Joyce as “some kind of sweaty, big-gutted man from Australia”. Joyce in turn mocked the conviction of Depp’s performance in the apology video.

The prime minister, Malcolm Turnbull, gave a playful response when asked if he would stand between his deputy – a former bush accountant with a colourful turn of phrase – and Depp by giving the Hollywood star a “pardon”.

“The pirate meets the cowboy ... maybe they could make a movie together,” Turnbull said on Triple M radio.