The outcome will underpin the post Brexit relationship between Britain and the EU
However, a British govenment source last night indicated that a no deal was more likely, after saying the EU offer on the table was "unacceptable".
Both parties continued talking into the night and will continue their discussions today.
Suzanne Byrne outlines principal sticking points in the talks:
'Despite it making up only a tiny part of the economies of either camp Fisheries has been at the top of the list of glaring disagreements. The EU wants maximum access for its boats to continue fishing in UK waters, where they currently catch about €655m worth of fish every year. Britain wants most of that business back, and says it will prioritise its own boats. Yesterday it emerged Royal navy vessels were on standby to patrol UK waters. The second issues related to rules on fair competition. If a post Brexit Britain cuts out the EU regulations it is used to adhering to, it can be cheaper to produce things, thus skewing the level playing field. The third issues revolves around how to resolve disputes after a deal is reached and what kind of sanction or penalty rule breakers will face. Analysts say the most likely route forward would be for the EU to compromise on the fisheries issue and the UK to blur some of its red lines on the level playing field. They have till midnight to reach a deal.'