Sunak arrived at a hotel on the outskirts of Belfast late on Thursday.
One European Union diplomat said it appeared a deal to revise the Northern Ireland protocol, agreed when Britain left the bloc to avoid a hard border with EU member Ireland, was close but not complete.
A separate meeting in Brussels on Friday between British Foreign Secretary James Cleverly and EU Brexit chief Maros Sefcovic would prepare for a possible rapid conclusion of weeks of intense talks, the diplomat said.
The meetings in Belfast with the region's main political parties underlined the fact that political support for any deal will be key to whether London and Brussels can finally put their post-Brexit spat over Northern Ireland behind them.
"What we want to hear ... most importantly, is where the negotiations have reached in removing the automatic application of EU law to Northern Ireland," senior Democratic Unionist Party (DUP) lawmaker Sammy Wilson told the BBC.
"That issue, that central issue of sovereignty and democratic deficit, has to be addressed."
Support from the DUP, Northern Ireland's largest pro-British party, is particularly crucial after it boycotted the region's devolved parliament in protest at the protocol.
Another senior DUP member said on Thursday they had not seen any details of the possible deal.
Opinion polls have consistently shown a majority of Northern Irish voters back the idea of the protocol but the imposition of checks on some goods arriving from the rest of the United Kingdom has sparked anger among many pro-British unionists.
The talks so far have been shrouded in secrecy, with some of the main players complaining that they have not seen any detail on the possible fixes to issues including the role of the European Court of Justice in Northern Ireland.
