The Prime Minister is also expected to speak to other EU leaders by phone before thrashing out a further delay to Brexit in Brussels.
The UK Government is seeking an extension to Article 50 no further than 30 June, although the EU is set to offer a much longer delay until the end of the year or beyond.
Meanwhile, some Conservative Brexiteers have voiced anger at the prospect of any further delay.
The Prime Minister’s visits on Tuesday make it unlikely that any compromise Brexit deal thrashed out with Labour will be put before MPs ahead of the summit, with no face-to-face talks currently scheduled with the official Opposition.
Downing Street said that “good-natured” dialogue with Labour had continued through the weekend, following a series of formal meetings last week, with both sides showing a “willingness to co-operate”.
“Our intention is engage further with the Opposition today and, given the need for urgency, we hope that will lead to further formal discussions,” she said.
The spokeswoman declined to set a deadline for a conclusion to negotiations with Labour, saying only that the Prime Minister wanted an agreement “as soon as possible”.
Tuesday’s weekly meeting of Cabinet has been cancelled due to Mrs May’s travels, with no rescheduled date yet announced.