European Commission President Jean-Claude Juncker has insisted that "we can have a deal" on Brexit ahead of the Halloween deadline.
But Mr Juncker was unable to put the prospects at more than 50/50 when asked by Sky News in an interview.
Mr Juncker met Boris Johnson in Luxembourg for Brexit discussions on Monday, before the prime minister headed for his ill-fated meeting with his Luxembourg counterpart Xavier Bettel.
The EU chief insisted his meeting with Mr Johnson was "rather positive", adding: "We can have a deal."
But when pressed by the broadcaster 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 added.
Mr Juncker reiterated that he had no "emotional relationship" with the 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.
Coveney says no Brexit breakthrough as EU needs credible proposals
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EC President @JunckerEU said he thinks a #Brexit deal can be reached by 31 October.— Sky News (@SkyNews) September 19, 2019
Speaking exclusively to @RidgeOnSunday, he also warned that a no-deal #Brexit would be "catastrophic" for Britain and for the EU.
Check out the full interview on #Ridge from 8.30am this Sunday. pic.twitter.com/8ahZ6X8l4K
Earlier, the British government has said Mr Johnson will not be bound by an "artificial deadline" to produce formal written proposals to resolve the Brexit deadlock.
Finnish Prime Minister Antti Rinne, following talks in Paris with French President Emmanuel Macron, said Mr Johnson should outline its Brexit plans to the EU by the end of September.
But a UK government spokesman said proposals would be put forward "when we are ready" and when Brussels is willing to "engage constructively on them".
Number 10 also confirmed that the UK had now shared, in written form, a series of "confidential technical non-papers" which reflect the ideas the UK has been putting forward.
Previously documents had been shown to Brussels officials but then taken back at the end of meetings for fear 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.
The spokesman said there had been "detailed discussions" in recent weeks with the European Commission's Taskforce 50 - the unit dealing with Brexit.
"We have now shared in written form a series of confidential technical non-papers which reflect the ideas the UK has been putting forward.
"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."
Brexit Secretary Stephen Barclay, who will meet Brussels' chief negotiator Michel Barnier tomorrow, warned the European Union against a "rigid" approach and suggested the final details of an alternative to the backstop may not need to be resolved until the end of 2020.
The European Commission confirmed it has received "documents" from the UK government on its Brexit proposals.
A spokeswoman said: "With regards to written proposals, I can confirm that we have received documents from the UK and, on this basis, we will have technical discussions today and tomorrow on some aspects of customs, manufactured goods and sanitary and phytosanitary rules.
"Then the discussion will also take place at political level because Michel Barnier, the commission's chief negotiator, will meet Steve Barclay on Friday."