The British Prime Minister and Brexit Secretary David Davis met Mr Juncker at 6am (7am local time) at the Commission HQ to hammer out a Brexit agreement.
After talks in Dublin on Wednesday night, 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.
EU Commission spokeswoman Mina Andreeva said on Twitter that they were "likely to meet this morning at 7:00 AM (0600 GMT) in the Berlaymont", the organisation's headquarters.
Tusk's role in the delicate choreography of reaching an accord had been to wait until May strikes a deal on making "sufficient progress" on divorce terms with Juncker's Brexit negotiator Michel Barnier.
The EU has been calling for clarity on three key issues - the Irish border, a financial settlement, and the rights of EU citizens in the United Kingdom - before it agrees to start trade talks on future relations.
And earlier on Thursday evening, a UK Government source said: "We're not there yet".
DUP leader Arlene Foster has said she is pleased there will be "no red line down the Irish Sea" and is glad to have confirmation that "the entirety of the United Kingdom is leaving the European Union, leaving the single market, leaving the customs union". "We will stay very firm".
Sinn Fein is to hold a protest in Rosslea on the Fermanagh/Monaghan Border on Saturday at 12 noon calling for designated special status for Northern Ireland post Brexit.
Barnier informed European Union ambassadors that Downing Street had told him a potential solution was being worked out that could possibly satisfy both Northern Ireland's Democratic Unionist Party (DUP) and Ireland, but that it had yet to be signed off by any of those involved, the Guardian reported on Thursday.
He rejected British media speculation that May could be given until next week to demonstrate "sufficient progress" on the three key issues of the Brexit divorce.
Meanwhile, Confederation of British Industry (CBI) president Paul Drechsler has underlined businesses' "immediate" need for a transition deal, warning that 60% of firms with Brexit contingency plans will put them into effect by Easter if Mrs May does not get the green light for trade talks next week.
Johnson said Wednesday that "the best way to sort it out is to get onto the second phase of the negotiations, where all these hard issues can be properly teased out, thrashed out, and solved".