Her spokesman said later that May was specifically referring to the type of deal the European Union is now offering on future trade, which Britain believes will split England, Wales and Scotland from Northern Ireland by insisting Northern Ireland adhere to different customs rules.
In a nod to the concerns of businesses, the plan backed by May's Cabinet on Monday (Sept 24) would also allow some access for low-skilled foreign workers, the newspapers said.
Speaking during her flight to the UN General Assembly in New York, Theresa May also hit out at Labour, saying the party would "accept any deal Europe gives, regardless of how bad it is for the UK".
The report was launched yesterday by leading Eurosceptics including David Davis, the former Brexit Secretary, and Jacob Rees-Mogg, and endorsed by Mr Johnson as a "real alternative" to Chequers.
Although the United Kingdom government is trying to reformulate the backstop proposal, the current wording would require Northern Ireland to remain in the customs union and the single market, separating it off from the rest of the United Kingdom by creating a customs border in the Irish Sea - something the prime minister has said she will never accept.
May said that "makes a mockery" of the Brexit vote, because Britain would still take orders from Brussels and there would be "uncontrolled immigration" from the EU.
Turning to Labour, Mrs May criticised comments made by the shadow Brexit secretary Sir Kier Starmer during the party's conference in Liverpool. "If they have issues with it, let's hear what those issue are", May said in an interview with CBS News, referring to the EU's response to the British plan.
"These blips in the world, they're blown a little bit out of proportion, but we double down, we don't throw our toys out the pram, hold our nerve, keep our cool", Raab said.
Earlier on Tuesday, Labour said it was likely to oppose any deal negotiated by Theresa May as it did not meet its six tests, lessening the chances of it getting through Parliament.
The Financial Times said that while ministers backed the advisers' proposals, the idea of giving no preferential treatment to European Union workers could change if Britain agrees a trade deal with the bloc.
'The FTA would only apply to the Great Britain-EU relationship, with Northern Ireland effectively remaining in parts of the single market and customs union, ' he said.