The members of the British government were told that the issue would hardly be discussed at the meeting beyond an update of the UK's preparedness for no deal.
Confirmation that a deal had been reached by officials follows months of protracted talks in Brussels, with measures to prevent a hard border on the island of Ireland having been the main stumbling block. France and Germany are understood to have made the point forcefully to Barnier.
"While there are still numerous hurdles ahead, sign-off on Wednesday could be a hugely important step toward getting a deal over the line before Christmas and avoiding a disastrous no deal scenario", said Craig Erlam, market analyst at OANDA.
The pound rallied on news of a deal, rising 1.5 per cent against the dollar to $1.3038.
The Prime Minister will warn her ministers that failure to approve the proposals will force the government and business to accelerate preparations for a no-deal Brexit.
But until now, all that has been agreed is a need for a backstop, so this deal should clarify how it'll be achieved.
His Conservative colleague Boris Johnson, the former foreign secretary, described the draft deal as "unacceptable", adding, "For the first time in a thousand years, this place, this Parliament will not have a say over the laws that govern this country".
Shaheen Afridi called up to Pakistan Test squad, Shadab, Zaman miss out
Ross Taylor has been the standout batsman for the Black Caps so far as he scored a match-winning century in the first game. Going by the experience of the conditions, Pakistan holds the advantage in the last game before the Test series starts.
"This is a calculated deceit on the British people", Mr Johnson told the Evening Standard.
The deal will be opposed by hard-Brexiteers such as Boris Johnson for making the United Kingdom a "colony", but is also already facing condemnation from Remain MPs.
Failure to meet that deadline would mean a deal can not be finalised until December. "No one deserves to be punished because of this Tory Brexit mess", the centrist Liberal Democratic Party's Brexit spokesman Tom Brake said.
Both Leave and Remain campaigners fear the deal - whose outlines are well known though it has not yet been made public - will be a limp compromise that fails to deliver either the letter or spirit of the Brexit the country asked for.
"We are clearly not out of the woods yet", the London-based Capital Economics research group said in a note to clients.
London suggested that until a wider trade deal is agreed that resolves the problem, Britain could temporarily stay aligned with the bloc's trade rules - as long as it can exit the arrangement when it wants.
By seeking to leave the European Union while preserving the closest possible ties, May's compromise plan has upset Brexiteers, pro-Europeans, Scottish nationalists, the Northern Irish party that props up her government, and some of her own ministers.
A British official voiced pessimism about the possibility of a breakthrough with the European Union this week due to continued deadlock on the issue of the border between British-ruled Northern Ireland and European Union member Ireland.