European Commission president Ursula von der Leyen has said "big differences remain" between the EU and Britain and "bridging them will be very challenging".
But she said "substantial progress" had been made on many issues in post-Brexit trade deal negotiations, following a phonecall with British prime minister Boris Johnson.
Earlier, Number 10 downplayed the chances of a breakthrough, suggesting it would only be a stocktake rather than a deal.
Minister for Foreign Affairs Simon Coveney has expressed hope that existing gaps between the EU and UK in the Brexit talks can be closed “through realism and a sense of fairness on both sides”.
He said “we believe that with political will there is now a path to a deal and welcome that the negotiating teams continue to make every effort to that end”.
Opening a Dáil debate on Brexit readiness for the end of the transition period, Mr Coveney said “fishing remains the most difficult issue to resolve and I hope the existing gaps can be closed through realism and a sense of fairness on both sides”.
The Minister re-iterated that “regardless of the outcome of the future relationship negotiations, hopefully in the coming days, the protocol means that the new customs and regulatory patrols coming into force for east-west trade will not apply to trade between Ireland and Northern Ireland.
He described this as “significant achievement” and reflected a key priority of the Government since the start of the Brexit negotiations.
Negotiations between the UK and EU continued this week after they were given the green light following a meeting between Mr Johnson and Dr von der Leyen last Wednesday.
Despite days of talks, Michael Gove, the British cabinet office minister, said on Thursday that the chances of an agreement remained “less than 50 per cent”.
He told the Commons Brexit Committee the “most likely outcome” was that the current transition period would end on December 31st without a deal.
“I think, regrettably, the chances are more likely that we won’t secure an agreement. So at the moment less than 50 per cent,” Mr Gove said.
Earlier, the European Parliament has issued an ultimatum to EU and UK negotiators, saying it will not ratify a deal by the end of the year if it is reached any later than this Sunday.
MEPs and chief EU negotiator Michel Barnier have warned that this would mean a short period of "no-deal" terms in which legally tariffs would have to be levied on trade between the EU and UK.
There has been some progress in the talks but the issue of fish is very much unresolved, Mr Barnier told MEPs, The Irish Times understands, warning that there needed to be a deal within days or there would be a period of no-deal.
"We give until Sunday to Boris Johnson to make a decision. The uncertainty hanging over citizens and businesses as a result of UK choices becomes intolerable," said Dacian Ciolos, the president of Renew Europe, the group in which Fianna Fáil sits.
“Michel Barnier and his team has our full support as we head to the Brexit moment of truth.”
In a joint statement, the heads of the parliament’s political groups said the parliament “stands ready to organise an extraordinary plenary session towards the end of December” to ratify a deal.
However, it would not do so if a deal came any later than Sunday, it warned, insisting that the parliament must have a copy of a provisional text “as soon as possible” to begin scrutinising it.
Manfred Weber, the head of the powerful European People's Party of Fine Gael, reiterated that a deal would only be ratified if it arrived by Sunday.
“After that we cannot reasonably scrutinise the deal before the end of the year. The agreement is too important to rush through parliament,” Mr Weber said.
National governments technically have the power to provisionally apply trade agreements until they are ratified, after a proposal by the European Commission.
However, the commission has long been warning that the alternative to ratification in December is a temporary period of no deal.
Nevertheless there would be significant pressure to do whatever possible to minimise the economic damage of no-deal terms, making for a potentially fraught political fight within the EU’s institutions. - Additional reporting PA
