EU sources have said a Brexit deal could be reached in the next 24 hours.
"There is an air of optimism", one EU diplomat told RTÉ News.
"The final touches are between [European Commission President Ursula] Von der Leyen and Boris [Johnson, the British prime minister]", a diplomat told RTÉ News.
The source said the Commission President was in touch with EU leaders.
"There's a very strong push to get it done before Christmas", the diplomat said.
"The idea that everyone comes back again on Sunday or Monday to start again … that will happen if necessary but there does seem to be a strong push to get it done before Christmas."
It is understood fisheries remains the final outstanding offer.
The EU appears to be sticking to the most recent offer of a 25% transfer of the value of fish caught by EU boats in UK waters to British fishermen.
Breaking: a meeting of EU ambassadors (Coreper) has been convened for tomorrow morning, to be briefed on Brexit negotiations, source— Tony Connelly (@tconnellyRTE) December 23, 2020
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Meanwhile, EU member states have started to prepare procedures to put in place the new trade deal with the UK from 1 January if one is agreed, three diplomatic sources told Reuters today.
During a meeting with the European Commission, which is negotiating with the UK on behalf of all the 27 member states in the bloc, national diplomats in Brussels were told to be ready for a meeting tomorrow, should a deal come.
"It seems the deal is pretty much there. It's a matter of announcing it today or tomorrow," said one EU diplomat.
They said the European Council, which represents the member states in Brussels, had started preparations to enable so-called "provisional application", a fast-track implementation of the agreement.
While both sides have said for days a deal is getting closer, the UK has been considerably more downbeat on the chances of getting there - let alone before Christmas - than the EU side.
Earlier, Taoiseach Micheál Martin said the gap on the remaining Brexit sticking point of fishing rights is still wide, but enough progress has been made that a deal is still likely.
"It is all down to fish," he said.
Speaking on RTÉ's Today with Claire Byrne, he said: "If you had a breakthrough tonight or tomorrow, officials in Europe could be working Christmas Day on the text.
"On balance, I think given the progress that has been made that there should be a deal. A no deal would be an appalling shock to the economic system on top of Covid-19."
He said it is a time of worry for fishing communities in Ireland and an honourable agreement that creates stability for this industry into the future must be reached.
The issue is not just about monetary terms, he said, but about sustainability and protecting many communities whose whole ecosystem is based on fishing.
Elsewhere, Minister for Transport Eamon Ryan has said that he hopes a Brexit deal can be reached by the end of today.
During a media briefing over Zoom Minister Ryan, who is self-isolating, said: "Hopefully we'll see a deal agreed by the end of today if reports are accurate on timelines.
"My sense is whatever the outcome of that we have to continue good collaboration with the UK."
He said he was working on maintaining co-operation with the UK in areas, such as energy and security, and developing climate action.
It emerged that there have been a number of phone calls in recent days between Ms von der Leyen and Mr Johnson, and these are expected to continue.
EU's chief negotiator Michel Barnier told member states that the UK's latest offer on granting European vessels access to British waters is not acceptable.
But he said the EU would give the negotiations a final push.
The European Parliament said the deadline has long since passed for MEPs to formally ratify an agreement, so any deal would have to be provisionally applied.
Both sides would have to agree to this, and getting provisional application over the line has its own procedural obligations.