British Prime Minister Theresa May's leadership is understood to be under fresh pressure after Tory MPs spent almost an hour in a private meeting discussing how to oust her.
Jacob Rees-Mogg, chair of the European Research Group, a faction within May's Conservatives, plans to vote against the Chequers deal but said that does not mean May has to go.
A spokesman for May declined to comment on the report.
Despite the more positive atmosphere surrounding the talks with the EU, UK prime minister Theresa May is facing a renewed threat from inside her own party.
Former Brexit Secretary David Davis, who quit the cabinet in July over May's European Union withdrawal plan, said: "I disagree with her on one issue - and it's this issue - and she should stay in place because we need stability and we need decent government".
The EU and Britain hope to clinch a deal later this year so parliaments on both sides can ratify it before Brexit.
European Commission head Jean-Claude Juncker said the EU will not allow Britain to participate only in some parts of the bloc's single market after Brexit without honouring all of the rules.
"It'll be in November, when parliament votes on the deal", she said.
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A number of MPs told how they had already submitted letters of no confidence to Sir Graham Brady, chairman of the 1922 Committee, and others discussed plans to follow suit.
Backbenchers told May's chief of staff, Gavin Barwell, the prime minister must "chuck Chequers" over a dinner at No 10. Under Conservative rules, a leadership election is triggered if 15% of Conservative lawmakers, now 48 of its 315 members of parliament, demand a vote of no confidence.
The Brexit European Research Group called for the government to agree "equivalence of United Kingdom and EU regulations" for agricultural products in order to keep the border open, and allow Brussels inspectors into Northern Ireland to check their implementation.
"We are working on a deal which will be good for United Kingdom industry and we are confident we're going to achieve that", a spokesman for May's government said.
On that occasion, the pound climbed close to 1% when Bloomberg reported that German officials were prepared to "accept a less detailed agreement on the UK's future economic and trade ties with the European Union in a bid to get a Brexit deal done".
Meanwhile, fellow former Conservative leader William Hague wrote in the Daily Telegraph that it would not be an exaggeration to say Britain could face "the most serious constitutional crisis in Britain for at least one century, possibly two" if a Chequers-based Brexit deal was blocked.
The comments came amid open warfare in the Tory ranks following former foreign secretary Boris Johnson's comparison of the Government's Brexit strategy to placing the United Kingdom in a "suicide vest" and handing Brussels the detonator.