Sources suggest a deal could be reached as early as next week on the region's post-Brexit trading arrangements.
Mr Sunak will meet local party leaders on Friday morning before heading on to Germany to meet EU leaders.
His Foreign Secretary, James Cleverly, will be in Brussels on Friday to meet the European Commission.
Mr Cleverly will meet European Commission Vice-President Marcos Sefcovic, the Foreign Office confirmed, saying it was part of "ongoing engagement and constructive dialogue with the EU to find practical solutions that work for the people of Northern Ireland".
The Northern Ireland Protocol is the trade deal that was agreed to ensure the free movement of goods across the Irish land border after Brexit.
It is at the heart of a political impasse in Northern Ireland, with unionist parties arguing that placing an effective trade border across the Irish Sea undermines the region's place within the UK.
The largest of those parties is the Democratic Unionist Party (DUP), which refuses to take part in Northern Ireland's power-sharing government - introduced in the 1990s as a way of ending decades of violence - unless its concerns are resolved.
Even though the DUP came second in May 2022 elections to Sinn Féin - a republican party that accepts the protocol - a new Northern Ireland government cannot be formed without its support.
The DUP has said it must be satisfied with any settlement before it agrees to return to power-sharing.
But the deal has split political opinion and the UK and the EU have been in lengthy negotiations about making changes to how it operates.
Ahead of Mr Sunak's visit, No 10 said: "Whilst talks with the EU are ongoing ministers continue to engage with relevant stakeholders to ensure any solution fixes the practical problems on the ground, meets our overarching objectives and safeguards Northern Ireland's place in the UK's internal market.
"The prime minister... [is] travelling to Northern Ireland this evening to speak to political parties as part of this engagement process."
After the meetings in Belfast the prime minister will travel to Munich for a security summit.