The Foreign Secretary’s calls to give residency rights to any illegal immigrants who have avoided detection for the past 10 years echo his controversial policy which he championed during his spell as London mayor.
Mr Johnson has reportedly argued his proposals would prompt the unregistered immigrants to start paying taxes and bolster the Treasury funds.
Estimates suggest there are as many as 1.1milion illegal immigrants living in Britain.
Yet the 52-year-old’s alleged plans have been met with fierce criticism by several Government figures, who claim the policy would entice more illegal immigrants to make their way to Britain.
A senior minister told the Sun: “It’s an insane idea and would make ordinary Brits furious.
“A lot of us round the table couldn’t believe Boris is still going on about this.
“Privately, Boris is still the most pro-immigration member of the Cabinet.”
Despite the uproar from some Cabinet members, Home Secretary Amber Rudd is thought to have shown interest in his plans, asking Mr Johnson for detailed proposals after the Immigration Implementation Taskforce meeting.
The Prime Minister – who served as Home Secretary under former Tory leader David Cameron – rejected immigration amnesties when she held Ms Rudd’s job and is thought to have been angered by Mr Johnson’s suggestions.
The latest spat comes after Mr Johnson turned up to a Cabinet committee with the wrong briefing notes – heightening fraught tensions within the Government about the direction of Brexit.
A spokesman for Mr Johnson said: “Boris reiterated what he has said publicly before about amnesties, including during the EU referendum campaign.
“He feels he has a moral responsibility to raise it, as it is what he believes.
“Any suggestion that there was strong disagreement expressed during the meeting is wrong.”
Yet a Home Office spokesman said: “We are not looking afresh at an amnesty for illegal migrants, and will not be.”
New quarterly immigration figures are set to be released imminently which are expected to show the number of new arrivals in Britain will be close to record levels.