May's decision to halt the vote came just hours after the EU's top court, the Court of Justice, said in an emergency judgment that London could revoke its Article 50 formal divorce notice with no penalty.
During the meeting, Juncker went on to say that the European Union was willing provide greater clarity over the Irish backstop plan to stop a hard border between Northern Ireland and the Irish Republic forming post-Brexit.
British Prime Minister Theresa May said earlier on Monday that the crucial parliamentary vote on her Brexit deal, originally scheduled for Tuesday, will be postponed, citing the acknowledgement that "the deal would be rejected by a significant margin".
The embattled British premier was due in Brussels later Tuesday for meetings with Juncker and EU Council President Donald Tusk, who will chair Thursday's summit.
"If we can't go forwards with her deal ... then I'm afraid the only way to change the policy is to change the prime minister and I really think it's her duty to go", Brexit-supporting Conservative Steve Baker said.
"That might include an addendum to the Withdrawal Agreement that sets out that Parliament will vote prior to going into a backstop, should that prove necessary, and potentially that the EU Parliament and UK Parliament must vote every year thereafter to provide that legitimacy for the UK to stay in the backstop, should that prove necessary", she told BBC Radio 4's Today programme.
He added: "I have no difficulty with statements that clarify what's in the withdrawal agreement but no statement of clarification can contradict what's in the withdrawal agreement".
May said on Monday that "nothing should be off the table", but warned that reopening the withdrawal agreement could see other countries seek to remomve bits they do not like, for example on fishing rights.
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But he added that "if used intelligently, (there) is room enough to give further clarification and further interpretations without opening the withdrawal agreement".
"The deal we achieved is the best possible".
"I will now do everything I possibly can to secure further assurances", May told mutinous MPs Monday on her dash to Europe ahead of the European Union summit.
Asked as he arrived at a meeting in Brussels what May can expect from Merkel, Deputy Foreign Minister Michael Roth replied: "I hope they will wish each other Merry Christmas, strength and all the best for the new year".
May will now fly to the Hague and Berlin Tuesday, to meet with Dutch Prime Minister Mark Rutte and German Chancellor Angela Merkel, but it remains unclear what, if any, compromises May can win that would satisfy critics within her own Conservative Party and their allies the Democratic Unionist Party (DUP). May has long refused calls to resign or put a second Brexit vote to the public.
According to the Guardian, Downing Street said the vote could be delayed till January, that reduces the time available to pass the necessary legislation to complete the UK's departure. "So I very much doubt that parliament will vote for the deal, when it has the chance to do so", he said.
Many MPs fear this arrangement could be in place indefinitely as the United Kingdom cannot pull out unilaterally.
European parliament president Antonio Tajani said: "It's good to have discussions, to meet with Mrs May but we won't be changing our position". Footage shows an assistant tugging on the door handle to little avail, while the Prime Minister sits in the backseat.