The prime minister and Ursula von der Leyen will meet in Berkshire in the afternoon to discuss "complex challenges" around the protocol.
The UK wants to change the current agreement - which sees some goods checked when entering Northern Ireland from the rest of Great Britain.
A new deal has been expected for days.
Deputy Prime Minister Dominic Raab earlier said the UK and EU were "on the cusp" of a deal and that the EU had "moved" on some issues.
Downing Street released more details about the talks between Mr Sunak and Ms von der Leyen, which is set to take place around late lunchtime.
If a deal is reached, it would then be announced later on Monday, with the leaders holding a joint press conference after the cabinet has been updated.
The prime minister would then address the House of Commons.
Both Tory and Labour MPs have been told by their respective whips to come to Parliament on Monday.
Downing Street said: "The prime minister wants to ensure any deal fixes the practical problems on the ground, ensures trade flows freely within the whole of the UK, safeguards Northern Ireland's place in our Union, and returns sovereignty to the people of Northern Ireland."
There have been "hundreds of hours of talks" during the "intensive negotiations with the EU", the spokesperson added, saying "positive, constructive progress has been made".
The Northern Ireland Protocol was agreed under former PM Boris Johnson as part of the process of the UK leaving the European Union.
It means Northern Ireland has continued to follow some EU laws so that goods can flow freely over the border to the Republic of Ireland without checks.
Instead, goods arriving from England, Scotland and Wales are checked when they reach Northern Irish ports.
Critics, including Northern Ireland's Democratic Unionist Party (DUP), feel this undermines the nation's position within the rest of the UK as well as impacting trade.
The DUP has complained about what it calls a "democratic deficit", with Northern Ireland being subject to EU rules while not having a say on them.
The party has prevented a Northern Ireland devolved government from forming, leaving it in political gridlock.
BBC chief political correspondent Nick Eardley said that while officials had been negotiating over the weekend, leader-level talks were needed to discuss the final details.
Sources in government have repeatedly said that not everyone will get everything they want from the deal - but the priority is addressing issues with the protocol and protecting the Good Friday agreement, our correspondent said.
There is no expectation in Westminster that the DUP will endorse the deal immediately and many believe it will not be enough to tempt them back to Stormont, he added.
Some Conservative MPs could also rebel against the government in any vote in Parliament, with Brexiteer Tories wanting lawyers to scrutinise the text.
One Tory told the BBC on Sunday night: "The bottom line is - if this doesn't result in power sharing, it's not a worthwhile agreement."
Taoiseach (Irish Prime Minister) Leo Varadkar said he had been in contact with Ms von der Leyen on Sunday and "very much" welcomed her meeting with Mr Sunak.
He tweeted: "We should acknowledge the level of engagement between the UK Gov, the European Commission and the NI parties in recent months."
His deputy, Micheal Martin, said there had been "very significant progress", adding "a great effort" had been made to resolve issues.
"I would hope it can be brought to a conclusion, but that's a matter for the UK and EU negotiating teams to call."
* Rishi Sunak and Ursula von der Leyen will meet late lunchtime for final talks in Berkshire
* There will be a cabinet meeting in the afternoon, where updates on those talks will be given
* If a final deal is agreed, the prime minister and Ms von der Leyen will hold a short joint press conference in the late afternoon
* The prime minister would then give a House of Commons statement on the agreement
The government has not confirmed if MPs would get a vote on any deal, but said they would be able to "express" their view.
Mr Sunak has been under pressure from some Conservative MPs over the role of EU law and the European Court of Justice in settling trade disputes.
Mark Francois, who heads the European Research Group of Eurosceptic Tory MPs, earlier said EU law needed to be "expunged" from Northern Ireland, bringing it in line with England, Scotland and Wales.
He told Sky News on Sunday that he had yet to see the detail of the deal and it would be "incredibly unwise" to bring in any new deal without giving MPs a vote.
DUP leader Sir Jeffrey Donaldson has previously said: "The objective in London and Brussels should be to get this right rather than rushed. The wrong deal will not restore power sharing but will deepen division for future generations."
The Northern Ireland Protocol is a trading arrangement, negotiated during Brexit talks. It allows goods to be transported across the Irish land border without the need for checks.
Before Brexit, it was easy to transport goods across this border because both sides followed the same EU rules. After the UK left, special trading arrangements were needed because Northern Ireland has a land border with the Republic of Ireland, which is part of the EU.
The EU has strict food rules and requires border checks when certain goods - such as milk and eggs - arrive from non-EU countries.
The land border is a sensitive issue because of Northern Ireland's troubled political history. It was feared that cameras or border posts - as part of these checks - could lead to instability.
The UK and the EU agreed that protecting the Northern Ireland peace deal - the Good Friday agreement - was an absolute priority.
So, both sides signed the Northern Ireland Protocol as part of the Brexit withdrawal agreement.
It is now part of international law.