"Logically that will happen once we have confirmation that we have reached "sufficient progress" and are going to begin the phase two process with the European Union", he said.
May had came close to a deal on Monday, but it fell apart at the last minute over the Irish border.
Commission chief Jean-Claude Juncker's chief of staff Martin Selmayr tweeted a picture of white smoke - the sign used by the Vatican to signify the election of a new pope - shortly after May's arrival.
"The Irish Prime Minister can be as unequivocal as he likes; we're also unequivocal in relation to these matters", DUP leader Arlene Foster told Sky News.
"Whatever way we devise for getting onto the body of the (Brexit) talks, it's got to be consistent with the whole of the United Kingdom taking back control of our laws, of our borders and of our cash", Johnson told reporters.
Britain agreed to pay a divorce settlement amounting to between 45 and 55 billion euros and to protect the rights of some three million European citizens living there after Brexit as part of the deal.
British Prime Minister Theresa May will face questions in the House of Commons today on the latest development in the Brexit talks.
After talks in Dublin, Irish Taoiseach Leo Varadkar and Dutch PM Mark Rutte made clear the European Union would not compromise and allow the Irish border to be kicked down the road to phase two of the talks, even under threat of Britain crashing out with no deal or divorce negotiations dragging on to 2018. May is struggling to balance those demands against the concerns of Northern Ireland's Democratic Unionist Party, which she relies on to support her government in Parliament.
On Thursday, EU Commission spokesman Margaritis Schinas had dismissed British newspaper reports that the Sunday deadline could be extended into next week as "not correct". Mr Varadkar said the decision to proceed to the next phase may not be taken until the new year.
Scotland's nationalist leader showed little patience, accusing the British government of being "totally and utterly incompetent" on Brexit.