The Prime Minister will travel to Luxembourg on Monday to meet Jean-Claude Juncker and said there is the “rough shape” of an agreement to be done. It will be Mr Johnson’s first face-to-face talks with the European Commission president since he took office and comes after a week of intense behind the scenes diplomatic activity. During a visit to Yorkshire, Mr Johnson said: "We are working incredibly hard to get a deal. There is the rough shape of the deal to be done.
"As some of you may have seen, I myself have been to talk to various other EU leaders, particularly in Germany, in France and in Ireland, where we made a good deal of progress.
"I'm seeing the President of the Commission and the chief negotiator Michel Barnier on Monday and we will talk about the ideas that we've been working on and we will see where we get.
"I would say I'm cautiously optimistic."
The working lunch at a “neutral location” with Mr Juncker will be a significant moment in the push to find a Brexit resolution.
Downing Street sources said the UK has been putting forwards ideas to Brussels and good progress has been made but there is still a long way to go before an agreement can be struck.
Mr Johnson and the Commission president are expected to discuss ways to resolve the deadlock over the Irish border backstop but No 10 does not expect the meeting lead to an immediate breakthrough.
The Prime Minister will stress how any deal must be able to win the support of Parliament, which rejected Theresa May’s EU exit package three times.
He will also hold talks with Luxembourg’s Prime Minister Xavier Bettel during the visit as he continues his diplomatic efforts to secure a new agreement before the next meeting of EU council leaders on October 17.
But Mr Johnson made clear that if he is unable to secure a new agreement he will not be deterred from meeting his “do or die” pledge to take the country out of the EU on October 31.
He said: “Whatever the shenanigans we will get on with delivering our agenda of preparing to take this country out of the EU on October 31.
“There will be ample time for Parliament to consider the deal I very much hope to do at the October summit on the 17/18.”
A European Commission spokeswoman said Mr Johnson had agreed to travel to Luxembourg to fit in around Mr Juncker's plans.
A European Commission spokeswoman said: "As President Juncker has said from the beginning, he was looking forward to working constructively with Prime Minister Johnson and it's just that they haven't managed to meet yet..
But the officials said she was "not going to speculate" on what Mr Juncker hoped to achieve from the talks.
The Eurocrat will give a speech to the European Parliament on Wednesday to update MEPs on Brexit.