The meeting follows talks that continued through the night between UK diplomats and Brussels officials aimed at resolving the bitter Brexit dispute over the Irish border.
The Prime Minister and her Brexit Secretary arrived at the Berlaymont shortly before 7am Brussels time (6am in the UK).
A European Commission spokeswoman said a news conference will be held after the leaders' meeting.
Hopes of a breakthrough after a week of wrangling were boosted yesterday after European Council president Donald Tusk announced he would make a Brexit statement at 7.50am today (6.50am in the UK).
Mrs May's bid to clinch a deal eluded her on Monday when it was blocked by Ulster's Democratic Unionist Party leader, Arlene Foster.
Amid a flurry of late-night diplomatic activity, Downing Street confirmed that the PM had spoken personally to Mr Juncker after he phoned the Irish Prime Minister, Leo Varadkar.
But more significantly - and perhaps crucially - the DUP's Westminster leader Nigel Dodds and the party's chief whip Sir Jeffrey Donaldson were seen emerging from 70 Whitehall, the offices of the PM's de-facto deputy, Damian Green.
Before briefing Ms Foster, who had remained in Northern Ireland, the DUP pair would not say whether they were ready to accept new proposals, with a tight-lipped Sir Jeffrey saying only: "Discussions are ongoing."
But, adding a note of caution, he said: "We are making progress but not yet fully there. Talks are continuing throughout the night."
Earlier on Thursday evening, a UK Government source said: "We're not there yet." But later a Number 10 spokesman said: "Discussions about taking forward the Brexit process are ongoing."
The significance of the precise timing of Mr Tusk's statement is that it is before the London Stock Exchange opens, which fuelled speculation that he will announce a deal giving the go-ahead for trade talks, which would send up share prices.
Mrs May, who has been accused of weakness after allowing the DUP - which is propping up her government in Westminster had been desperate hoping to make a new offer on the Irish border by the end of this week.
The DUP objected to what is known as "regulatory alignment" between Northern Ireland and the Republic, which the party claimed would mean maintaining a soft border and a new frontier with the UK mainland in the Irish Sea.
Time has been running out for the Prime Minister as she attempts to do a deal to allow leaders at the European Council summit on 14 December to declare "sufficient progress" has been made on divorce issues so trade talks can begin.
An Irish Government spokesman said: "Matters are being considered as part of ongoing discussions involving the (EU negotiating) Task Force, the Irish Government and the British Government."
Earlier, Ireland's deputy prime minister Simon Coveney said the Dublin government would consider alternative proposals from London, but stressed it would not countenance anything that fell short of the assurances it needs over the shape of the border post Brexit.
"We are in a position where we still need to find a way forward but, let me be very clear, the core issues that Ireland got agreement on at the start of this week are not changing," he said.
And the UK Foreign Secretary and leading Cabinet Brexiteer Boris Johnson insisted any deal must stick to the spirit of the Leave campaign.
"It is very, very important that whatever happens now, whatever we agree, has got to be consistent with taking back control of our laws, of our borders and of our cash," he said.
Pressed by Sky News on whether he was comfortable with a widespread regulatory alignment between the UK and EU after Brexit, the Foreign Secretary said: "You can take it from me that whatever comes up, whatever the solution that we come to, whatever we devise getting on to the body of the talks, it's got to be consistent, it's got to be consistent with the whole of the United Kingdom taking back control."