But the European Commission president was unable to put the prospects at more than 50/50 when asked by Sky New.
Mr Juncker met Boris Johnson in Luxembourg for Brexit discussions on Monday, before the Prime Minister headed for an ill-fated meeting with his Luxembourg counterpart Xavier Bettel.
But when pressed by the broadcaster in the interview broadcast on Thursday if the chances were more than 50/50, he replied: "I don't know."
He assured that he is "doing everything to have a deal" because he wanted to ward off a no deal with "catastrophic consequences".
"It's better for Britain and for the European Union to have an organised deal," he said.
Mr Juncker reassured that he has no "emotional relationship" with the Irish backstop, which aims to prevent a hard border returning to the island of Ireland but has been a major sticking point to getting a deal through Parliament.
"If the objectives are met - all of them - then we don't need the backstop," he added.
The pound reached a two-month high following Mr Juncker's comments.
He also confirmed he had received documents from Mr Johnson outlining draft ideas for a fresh withdrawal agreement late on Wednesday night.
Downing Street had said the UK shared a series of "confidential technical non-papers", which reflect the ideas being put forward.
Previously documents had been shown to Brussels officials but then taken back at the end of meetings out of fears they would be leaked.
But a "non-paper" is not a formal Government position and falls far short of what has been demanded by Brussels.
Meanwhile, Stephen Kinnock, a key MP in cross-party efforts to get a deal, said he was feeling "relatively, cautiously optimistic" after meeting with EU chief negotiator Michel Barnier in Brussels on Thursday along with Labour colleague Caroline Flint.
Mr Kinnock told BBC's Newsnight that pressure for a new divorce pact was "ramping-up" because of growing concern of a "catastrophic no-deal crash-out" and limited options for the PM.
The PM was under pressure from Finnish prime minister Antti Rinne to formally outline his plans to the EU by the end of this month.
Mr Rinne told reporters after meeting French president Emmanuel Macron that they "agreed that it is now time for Boris Johnson to produce his own proposals in writing - if they exist".
"If no proposals are received by the end of September, then it's over," Mr Rinne said.
The Government insisted Mr Johnson will not be bound by an "artificial deadline" to produce formal written proposals to resolve the Brexit deadlock.
Mr Johnson said progress was being made, but the extent of it should not be exaggerated.
"You heard Jean-Claude Juncker yesterday say that he doesn't have any emotional attachment to the backstop," Mr Johnson said.
"Now that is progress - they weren't saying that a month ago."
But Ireland's deputy prime minister Simon Coveney said a "big gap" remains between the UK and the bloc.
"And in order to close that gap we need to get credible proposals from the British government which we simply haven't received yet," he said.
A UK Government spokesman said there had been "detailed discussions" in recent weeks with the European Commission's Taskforce 50 - the unit dealing with Brexit.
"We will table formal written solutions when we are ready, not according to an artificial deadline, and when the EU is clear that it will engage constructively on them as a replacement for the backstop," he said.
Brexit Secretary Stephen Barclay, who will meet Mr Barnier on Friday, warned the European Union against a "rigid" approach and suggested the final details of an alternative to the Irish backstop may not need to be resolved until the end of 2020.
The backstop - the contingency measure to keep the UK closely aligned to Brussels's rules in order to prevent a hard border with Ireland - is seen as the main stumbling block to a deal.
Mr Barclay said the PM had shown he was willing to be "creative and flexible" by considering an all-Ireland approach to plant and animal checks and suggested that it was now for the European Commission to shift its stance.