"Taking all of this together, 95 per cent of the Withdrawal Agreement and its protocols are now settled", she will say, according to excerpts from her statement to parliament.
Grumbling has grown since she suggested at an European Union summit last week that Britain could remain bound by the bloc's rules for two years or more during a transition period after it leaves on March 29, to help solve the border problem.
But that fraction is the hardest bit - the issue of the Northern Ireland border.
The EU proposed a backstop that would mean Northern Ireland staying in the EU customs union, large parts of the single market and the EU VAT system, while the rest of the United Kingdom left. May opposes this because, she argues, it amounts to splitting the United Kingdom into different customs zones, which would be politically unacceptable.
But asked if the source should be unmasked and punished, Francois said he was not going to tell the Conservative Chief Whip Julian Smith "how to do his job".
Barnier said other backstop measures were needed to prevent unauthorized Irish imports of goods such as chlorinated chicken, produced in the US but outlawed by European Union food standards. May will say that the shape of the deal across "the vast majority" of its text is now clear.
While willing to consider extending the UK's transition period beyond 2020, she said this was "not desirable" and would have to end "well before" May 2022.
The original plan is for a 21-month period starting March 30, 2019, as soon as the United Kingdom has left.
Mr Raab said the longer transition period should be negotiated instead of, not as well as, the backstop.
Marchers chanted "People's vote!" and brandished signs with slogans like "bollocks to Brexit", "the wrexiteers" and "Brexit stole my future". CNN could not independently verify the number of marchers.
Brexit deal is 95% settled, UK's May to tell Parliament
Government analysis of a no-deal Brexit shows it would be disastrous for the economy and British business, and even lead to food and medicine shortages. These options are a million miles away from what was promised. "The government doesn't have a mandate to gamble with our future", London Mayor Sadiq Khan, a prominent anti-Brexit voice, told the crowd.
Organizers handed out postcards for people to write to their local lawmakers demanding a final say on the Brexit deal, rather than relying on Parliament to approve it.
Theresa May will step in front of MPs, reporting on her Brexit talks achievements, having faced harsh rhetoric and bitter bickering from hard-core Brexiteers within her party in the past few days.
Tory MP Johnny Mercer said he has received "overwhelming" support from within the party since he described the government as a "shitshow".
Downing Street told CNN it would not be commenting on Mercer's interview.
The Belgian liberal MEP, who is meeting Home Secretary Sajid Javid regularly, said he is also pushing for improvements on citizens' rights after Brexit and may bring forward a resolution on the issue in the coming weeks.
"It seems to be getting ever more precarious", he said.
Criticism of her Brexit strategy has intensified following a Brussels summit.
Brexit Secretary Dominic Raab said the exit agreement must be finalised by the end of next month to allow new laws to be put in place in time for exit day.