Mr Juncker said: “I have reason to think that the rapprochement potential between both sides has increased in recent days.”
However government sources believe the EU is just attempting to put pressure on Prime Minister Theresa May to agree on a compromised set of terms for the withdrawal agreement.
A government source said: “This is classic EU tactics – trying to ramp up pressure and expectation ahead of the October meeting.”
However, reports of a deal being close between the UK and EU appear wide of the mark, after Brussels were unwilling to accept many aspects of Mrs May’s Chequers plan at the last EU summit with the 27 EU leaders in Salzburg two weeks ago.
President of the European Council, Donald Tusk criticised Mrs May’s proposed economic partnership saying it “will not work” as it would undermine the single-market.
One of the main disagreements blocking a deal remains the issue of the “Irish backstop” and how to avoid a hard border in Ireland.
The Irish Government yesterday called on Mrs May to break the deadlock with the EU before the next crucial meeting.
Dublin’s Europe minister Helen McEntee told BBC Radio 4’s Today programme: “We have 10 days between the teams to negotiate and we have seen what has happened in a short space of time previously. I think where the will is there it can be done, and I do believe the will is there.”
But in a warning to Mrs May, Nigel Dodds, the DUP’s Westminster leader, said they will not tolerate “tariffs, checks or anything else between one part of the UK and the other”.
In an in-depth interview, Mr Juncker also suggested the result of the referendum in 2016 could have been different if the then Prime Minister David Cameron had not asked him to stay away.
Mr Juncker said: “If the Commission had intervened, perhaps the right questions would have entered the debate.”
“At that time it was already clear to us to what trials and tribulations this unfortunate vote of the British would lead to. I’m always amazed that I’m always blamed.”
The President of the European Commission also blasted the British press claiming “they do not respect the human rights of political actors at all” he also added: “I will not miss it.”