Mr Barnier, who yesterday briefed the EU General Affairs Council in Brussels, is now set to demand "credible" guarantees from Theresa May that any future deal could not be unpicked by one of her successors.
A declaration on trade will most likely reflect the to opposing views of Barnier and the French President Emmanuel Macron, who are both pushing for a detailed roadmap for the bloc over fears that May's government will push to radically alter the terms agreed once Brexit becomes official in March of next year.
Britain is "cautiously optimistic" of striking a Brexit deal with the European Union "but there is a lot of work to do to get there", Foreign Secretary Jeremy Hunt has said.
He branded Mr Barnier's "backstop" proposals - which would see Northern Ireland remain in the European Union customs area - unworkable, because they would create a border in the Irish Sea and fail to respect the constitutional integrity of the UK.
Mr Hunt said Mrs May would speak for the whole country following his predecessor Boris Johnson's public criticisms of her Chequers Brexit blueprint.
Speaking to Panorama, the prime minister said that if Parliament does not ratify her Chequers plan, "I think that the alternative to that will be having no deal".
Mr Varadkar added: "It is fair to say that some of the things I have been reading in the British papers, particularly the British-owned papers, are very far off the mark when it comes to the reality of what is going on at the minute with these negotiations".
The Irish border issue is the biggest barrier to reaching such an agreement, the committee said.
The EU have said the economic pillars of the Chequers plan - United Kingdom participation in the single market for goods and a customs arrangement which would see the United Kingdom collect tariffs for the EU - are "unworkable".
Leaving the EU in March 2019 without having signed a withdrawal agreement would be "chaotic and damaging" for the United Kingdom, the Exiting the EU Committee said in a report that appeared to challenge the government's claim it is close to reaching a deal.
The plan has come under fierce scrutiny, including from Conservative Brexiteers and the DUP who claim it will lead to a sea border.
Opponents of May's blueprint claim leaving the European Union - the U.K.'s biggest trading partner - without a free-trade agreement would be preferable because Britain would be free to strike new trade deals around the world.
"I don't want manufacturers to feel that they've got to operate under all sorts of different rules, because that complicates life for them and that potentially means business leaving this country", she said.