Disputes over fishing rights and future business competition rules have been the major hurdles to agreement during months of often fraught talks.
But BBC political editor Laura Kuenssberg said Downing Street now seemed “very confident” of a deal.
Negotiators are now thought to be thrashing out the final details.
The official announcement of a deal is expected on Thursday morning.
The document is thought to be around 2,000 pages long, with both sides having until 31 December – when the UK leaves EU trading rules – get it approved by parliamentarians.
A deal would end the prospect of the two sides imposing widespread import taxes – tariffs – on each other’s goods from 1 January, which could have affected prices.
EU sources said the UK prime minister and European Commission President Ursula von der Leyen had been in contact in an attempt to break the deadlock before the expected pause in negotiations for Christmas.
- Brexit happened but rules didn’t change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards – they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
What happens next with Brexit?
The UK has insisted on having control over fishing in its waters from 1 January and retaining a larger share of the catch from them than under the current quota system.
But the EU wanted to phase in a new fishing system over a longer period and retain more of its access to UK waters for boats from France, Spain and other member states.
UK ministers have repeatedly ruled out any extension to the transition period, under which the UK has continued to follow Brussels’s trade rules since it left the EU on 31 January.
The sides also disagreed over whether UK firms should continue to follow the same rules as companies within the EU – and on how future trading disputes should be resolved.
The European Research Group of Brexit-supporting Conservative MPs has promised to reconvene its “star chamber” of lawyers – which was highly critical of previous Prime Minister Theresa May’s withdrawal agreement with the EU – to analyse any deal that is reached.
Chairman Mark Francois and deputy chairman David Jones said it would “scrutinise it in detail, to ensure that its provisions genuinely protect the sovereignty of the United Kingdom”.