Ms Heard escaped conviction and the pair released an unusual apology video.
But legal documents filed in a US court allegedly show Mr Depp was "fully aware" he was breaking Australian laws.
His former business managers, The Management Group (TMG), claimed the actor had "pressured one of his long-term employees to 'take the fall'," in papers obtained by People.
'It is called perjury'
Australian Deputy Prime Minister Barnaby Joyce subsequently hinted that the government may reinvestigate Depp.
"If the allegation is correct, there's a word for that - it is called perjury," Mr Joyce told the Australian Broadcasting Corp.
"We're an island continent and we take biosecurity very seriously and it doesn't matter if you think that you're Mr Who's Who of Hollywood, you're going to obey our laws."
Mr Joyce made international headlines two years ago when he said the dogs - Pistol and Boo - should "bugger off back to the United States" or risk being put down.
Mr Depp fired back referring to Mr Joyce as some kind of "sweaty, big-gutted man from Australia".
Last year, Ms Heard pleaded guilty to falsifying her immigration papers and was placed on a A$1000 (£600, $760) one-month good behaviour bond.
Her lawyer argued the actress thought Mr Depp's assistants had already sorted out the dogs' travel documents for their journey to Queensland two years ago.
Australia's tough quarantine laws are designed to keep disease at bay.
Earlier this week, Mr Depp apologised for remarks which appeared to threaten US President Donald Trump during a speech at the UK's Glastonbury Festival.
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