May's office says today's trip is aimed at encouraging the pro-British and Irish nationalists of to resolve their differences.
There's now hopes a deal to resume power sharing could be done as early as this week.
"We are serious about [restoring] functioning power-sharing", she said, adding that her party held no talks with the rival Democratic Unionist Party on Monday.
Get latest news & live updates on the go on your pc with.
Following talks with Theresa May in Belfast, Mr Varadkar said both governments agreed that was the best approach and officials would "explore solutions" to the issue over the coming weeks and months.
Irish Prime Minister Leo Varadkar said he is "very hopeful" of an agreement being reached this week.More news: Snapchat faces backlash after app redesign
More news: Truly best in show: Westminster victor making Broadway debut
More news: Woman suffering from rare disease, wakes with British accent
'There is the basis of an agreement and it should be possible to see an executive up and running in Northern Ireland very soon'.
It will be the first time the prime minister has been to Northern Ireland since July 2016 when she met the then first minister Arlene Foster and deputy first minister Martin McGuinness.
He said talks were at a critical stage and the party was focused on achieving a deal.
Newly-appointed Sinn Féin president Mary Lou McDonald will join her party's negotiating team at Stormont, however, it is understood that Tanaiste Simon Coveney will not travel north until later in the week.
"We have always said, and this is where the British and Irish governments are very much agreed, that the best way to achieve that is in the context of a new relationship between the United Kingdom and EU".
While both parties have acknowledged that progress had been made, a DUP source has played down expectations of a deal being finalised on Monday, suggesting to the Press Association that if an agreement does materialise it is more likely later in the week.
Sinn Fein wants a standalone piece of legislation to protect speakers - an Irish Language Act - but the DUP has long insisted it would only consider new laws if they also incorporate other cultures, such as Ulster Scots.