May said she would not accept a customs border in the Irish Sea.
"Taking all of this together, 95% of the Withdrawal Agreement and its protocols are now settled", she said.
The transition period is due to expire at the end of 2020 - with Mrs May insisting that an extension should only last a few months if one is necessary.
Ms Flint told the Yorkshire Post: 'There are a number of Labour MPs who feel if there's a reasonable deal on the table, if you're going to say no you need some bloody good reasons why if we're going to end up with no deal.
She urged the European Union to do more to ensure commitments entered into by both sides to avoid a hard border between Northern Ireland and the Republic of Ireland were honoured by whatever means necessary.
"All of this, from the last three weeks alone, is in addition to the agreements we had already reached", she will say.
Jack Blanchard for Politico writes that divisions over Brexit have turned the party into "a powder keg", with open talks of an imminent vote of no confidence against May, and "the feverish atmosphere led at least one MP to brief Sunday newspapers in, frankly, terrible terms".
But Tories and DUP would not as "that would be Turkeys voting for Christmas", she said.
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Last December and in March this year, the United Kingdom committed to the inclusion of an "all-weather" protocol in the withdrawal agreement that would ensure a hard border on the island of Ireland would never return under any circumstances.
"But in any such scenario we would have to be out of this implementation period well before the end of this parliament", she added.
An early offer of an EU-UK customs arrangement, note EU officials, also runs a risk of angering Britons who want to hold May to her rejection of a customs union.
While the speech is likely to contain no new policy announcements, it will likely provoke suspicions among restless Brexiteers that May has made more secret concessions in Brussels to get a deal over the line.
Building an "all-UK customs element" into the treaty to be finalised soon would, European Union officials argue, lend May credibility for her insistence to critics at home that Northern Ireland will never need to be treated differently from the mainland.
In a separate statement, Brexit Secretary Dominic Raab said the "meaningful vote" on the final Brexit deal could not be allowed to prevent or delay the UK's departure from the EU.
According to the Financial Times, some ministers also reacted in disbelief when they were told that in the event of a no-deal Brexit, the government plans to charter commercial ships to bring in emergency medicines and food.
On Wednesday, May will face another showdown with her party, this time confronting a gathering of the 1922 Committee of rank-and-file Tory members of Parliament, who will challenge her strategy afresh.