Meanwhile, the UK's chief negotiator says the Government is not afraid to walk away from Brexit talks without a trade deal.
According to Johnson, if the two sides don't agree by 15 October there will be no free trade agreement, and they "should both accept that and move on".
"So a lot of what we are trying to do this year is to get them to realise that we mean what we say and they should take our position seriously".
"We came in after a government and negotiating team that had blinked and had its bluff called at critical moments and the European Union had learned not to take our word seriously", negotiator Frost told the British newspaperThe Daily Mail on Sunday. "If we can reach an agreement that regulates trade like Canada's, great".
Irish Foreign Minister Simon Coveney, who played a key role in negotiating the withdrawal agreement and Northern Ireland protocol, said on Twitter that the reported move "would be a very unwise way to proceed".More news: Fortnite-gate: Google Will Attempt to Have Epic's Antitrust Lawsuit Dismissed
Sections of the bill - which is expected to be published on Wednesday - will explicitly say the United Kingdom government reserves the right to set its own regime in areas including state aid and Northern Ireland customs, directly setting up United Kingdom law in opposition with obligations under the withdrawal agreement, the Financial Times reported last night.
Environment Secretary George Eustice has admitted that there are "legal ambiguities" in the Brexit divorce deal, after it emerged that ministers are planning legislation which would override key parts of the withdrawal agreement.
Lord Frost had a similar message as he and Mr Barnier prepare to enter the final phase of their negotiations on trade when formal discussions resume on Tuesday.
"We will have full control over our laws, our rules, and our fishing waters", Mr Johnson will say.
"We will always reserve the right to act in the best interests of Northern Ireland and the UK's internal market", it said in a statement.More news: Hong Kong police arrest about 290 protesters
Trade associations representing British freight haulers and storage companies are asking for urgent talks with government leaders to allay concerns over preparations for Brexit, that may threaten supplies of critical goods caused by border controls and computer systems.
They said it was "not meant to derail the talks", but a key European Union diplomat told the BBC it was "a self-defeating strategy" that could lead to the trade talks unravelling altogether.
"We will have the freedom to do trade deals with every country in the world".
'Given the Withdrawal Agreement & Political Declaration David Frost negotiated last autumn were 95% the work of his predecessors - and the 5% that was new involved giving in to the EU's key demand (for some customs processes when goods move GB to NI) - that quote's some brass neck, ' he wrote.
He added: "It would be the most reckless act that a British government, and they've made many reckless acts in Ireland.in a long, long time and if they do this their worldwide credibility I think would be shot to pieces".More news: Novak Djokovic disqualified from the US Open