'There is a lot of hard work ahead, there will be more difficult moments as we enter the final stages of the talks, but I'm convinced we will secure a good deal that is in the interests of the United Kingdom and of the European Union, ' she said.
British Prime Minister Theresa May and other European Union leaders voiced renewed confidence on Thursday they could secure a Brexit deal, saying they were working hard to overcome the hurdles that only days ago brought the talks to a halt.
Addressing MPs in the House of Commons on Monday, May had said a deal was "achievable" while sticking to her principles on the Irish border issue.
"She acknowledged that there were a few significant issues that were still outstanding, but said that the very real sense she had from leaders around the table at the council was that they wanted to reach a deal as soon as possible this autumn", a No 10 spokesman said.
If agreed, the change would mean the United Kingdom remaining within the single market and customs union and subject to EU rules and regulations for nearly three years after the official date of Brexit in March 2019 and more than five years after the referendum vote to Leave.
Less than six months before Britain quits the European Union in its biggest shift in policy for more than 40 years, the two sides are at odds over how to deal with their only land border, between the British province of Northern Ireland and Ireland.
"A further idea that has emerged, and it is an idea at this stage, is to create an option to extend the implementation period for a matter of months, and it would only be a matter months", she told reporters on the second day of an European Union summit.
Irish Prime Minister Leo Varadkar summed it up by saying "big gaps" remained between the two sides "both in terms of the shape of the future relationship and also the protocol on Northern Ireland and Ireland and the backstop".
The LBC presenter and former Ukip leader was fuming that the Prime Minister may agree to extend the transition period beyond 2020. But the problem is we can not have a border in Ireland between the Republic and the province [of Northern Ireland].
"When you go back again and say "hang on it might not even be December 2020", why should we believe anything the Government says if they carry on like that?"
Simon Collins, the Executive Officer of the Shetland Fishermen's Association, warned the Government it should not let fishermen down again - insisting the key issue between the fishing industry and the UK Government remains to be "trust" in Brexit talks.
The East Antrim MP said Mrs May should not have agreed to settle the so-called "EU divorce bill", or signed up to the backstop proposals.
A November summit could be used to focus on preparations for a no-deal Brexit.
And one person familiar with the discussions said May's Tory party would find it hard to be fighting the next general election - due in 2022 - while the country is still inside the single market and customs union.
Theresa May and her European Union counterparts seem likely to trot out the line that a Brexit deal will, probably, be struck, albeit at the 11th hour at this evening's European Union summit.
In a radio interview, Boles said he feared May was losing the confidence of people who have been supportive of her throughout this process.
"A further idea that has emerged is to create an option that extends the implementation period for a matter of months", May told reporters in Brussels on Thursday. "May is a positive political message: we want to achieve an agreement", Tajani said. "If they knew the negotiations were being pushed right up against the next election, why would they be conciliatory in these negotiations?"
But any extension will need to take into account concerns on both sides to avoid the transition ending with no deal.
Leaders of other member countries said the real fight was not with the European Union. but within May's fractured Conservative Party.