The people said they expected Johnson to drop, or dilute, the most hard sections of the law if he secures an overarching trade deal with the European Union, potentially as part of the negotiations with the bloc.
Gove said the door "is ajar" for EU Chief Negotiator Michel Barnier to come to London next week to continue negotiations before the transition period expires at the end of the year. "The EU have effectively ended them by saying that they do not want to change their negotiating position", the spokesman said.
Downing Street said that Mr Barnier should "only come to London next week if you are prepared to discuss all issues" and that the United Kingdom should not be "required to make all the moves", adding: "If not, there is no point in coming".
"Or he is willing to discuss the practicalities of areas such as travel and haulage, which the PM mentioned in his statement".
A member of the EU Parliament has told LBC that following the Prime Minister's latest comments on Brexit, it seems as though he never wanted to agree on a deal.
On Friday, Boris Johnson accused European leaders of having "abandoned the idea of a free trade deal" and told the country to "get ready" for a no-deal outcome in the negotiations after his Oct 15 deadline for reaching an agreement passed.
A so-called "Australia deal" means that the United Kingdom would trade on World Trade Organization terms: as a country without an European Union trade agreement, like Australia, tariffs would be imposed under WTO rules, likely causing significant price rises.
"At the same time they have insisted we accept a level of control over our autonomy that an independent country can't really accept and that they should have exactly the same access to our fishing waters".
"Given that they have refused to negotiate seriously for much of the last few months, and given that this summit appears explicitly to rule out a Canada-style deal, I have concluded that we should get ready for January 1 with arrangements that are more like Australia's based on simple principles of global free trade".
However, industry reacted with alarm, warning of the damage to an economy already stricken by coronavirus if there was no deal by the end of the year.
In a round of broadcast interviews on Sunday, Gove said that the door was still "ajar" for talks, but he was less hopeful than he had been in recent weeks that a new trade deal will be reached.
"Neither side can afford to fall at the final fence".
It comes as business said a deal was vital to help the post-Covid recovery.
European Commission President Ursula von der Leyen said she was keen for a deal, though Macron was more downbeat. "We hope the European Union will change their position and we are certainly not saying if they do change their position we can't talk to them".