A Brexit trade deal was close to being agreed last night after nine months of intense negotiations.
It would guarantee the EU and UK tariff-free access to each other's goods markets and fishing waters and ensure ongoing transport, energy, police and security links.
One diplomat said that while there was "no deal just yet", the prospect was "not without hope".
Another said there was "genuine" optimism.
"After nine months of gestation, surely it's time something's delivered," said one EU source.
However, talks were continuing well into last night to try to lock down a deal on fisheries - the most intractable issue in the talks.
Although it contributes less than 2pc to the bloc's economy, fishing is a totemic issue for Ireland and several other EU countries, including France, Spain, the Netherlands, Belgium and Denmark.
The EU believes its continued access to UK waters goes hand in hand with the UK's demand for access to the bloc's single market.
Negotiators had grown far apart on fisheries at the weekend, but a phone call between European Commission president Ursula von der Leyen and British prime minister Boris Johnson on Monday helped get them back on track.
The UK wanted to claw back up to 60pc of the value of the EU's annual catch in its waters over three years, while the EU had suggested giving up 25pc over six years.
The two sides had also been squabbling over how - and in what sectors - the EU would be able to retaliate if it believes the UK has undercut it on product standards, state aid or fisheries.
EU lead negotiator Michel Barnier told MEPs this week that both sides would consult each other and an independent arbitration panel before taking any retaliatory measures.
The final text of a deal is expected to run to between 1,000 and 2,000 pages and cover not only goods and fisheries but matters such as social security, police cooperation and data protection.
A deal was reached some time ago on visa-free travel and health coverage for stays of up to 90 days.
The UK will also retain access to EU criminal records, terrorist DNA, fingerprint and vehicle registration databases.
However, it was unclear yesterday when the EU would adopt "equivalence" decisions allowing UK financial services providers to continue operating in the bloc.
The EU has also invited UK universities to participate in its student and teacher exchange programme, Erasmus, but the UK has not confirmed if it will take part.
Trade talks were escalated to leaders' level this week after EU and UK teams exhausted all their options.
With a week to go until the end of a post-Brexit transition period, there had been a real risk of a no-deal period on January 1.
That could have meant chaos at UK and European ports, which saw a preview this week after France closed its borders to UK hauliers, fearing the spread of a new virus strain.
EU officials are now fast- tracking a legal process to ensure the deal applies provisionally from next month, pending approval by the EU and UK parliaments.
There is not enough time left for the European Parliament to vote on the text before the Brexit transition period ends on December 31.
"All of the things necessary for a proper political process are not possible for the time being," said German MEP Martin Schirdewan, a member of the European Parliament's Brexit coordination group.
"Those who should take the political decision and give their consent are not even aware of the details."
The deal will also need to be endorsed by the EU's 27 governments.
The European Union's chief Brexit negotiator Michel Barnier is involved in last-gasp talks with UK