The Minister for Foreign Affairs, Simon Coveney, has said neither of two remaining obstacles in relation to Brexit are easy to resolve.
He said while he is hopeful that it can result in a successful agreement, "we have to be ready for both outcomes".
Speaking on RTÉ's News at One, Mr Coveney said "because the negotiating teams have gone really quiet here, there are no briefings out to the media, that's an indication to me that there's a serious, if difficult negotiation continuing".
He said he has always been optimistic a deal is possible and that it makes no political or economic sense for the EU and the UK not to have a future agreement in place because of all of the disruption would cause to economies and political relationships.
He said "the motivation here given the cost of failure is to get a deal done".
Mr Coveney said the two key issues "fair competition and a level playing field around for now and in the future is a really difficult issue to resolve". But he said his understanding is that "some progress" is being made in that area and in relation to fishing.
He said it is a different issue but equally difficult to resolve because "it's highly emotive and highly political and within the UK is linked to the expression of sovereignty that comes with Brexit".
Post-Brexit trade deal negotiations between the UK and EU are continuing in Brussels amid reports that progress in the talks could see a deal agreed this week.
The EU's chief negotiator, Michel Barnier, is said to have told diplomats the UK had moved towards the bloc's demands on the level playing field, according to the Daily Telegraph.
It said Mr Barnier told ambassadors the UK accepted a "rebalancing mechanism", meaning it could face tariffs if it moves too far away from EU rules.
The Guardian reported that European Commission president Ursula von der Leyen said there had been "movement" and talks were "on the very last mile".
Negotiations between the two sides were extended on Sunday after Boris Johnson and Mr von der Leyen agreed to continue the process despite major differences remaining.
Mr Barnier updated diplomats from the 27 EU states about the progress before resuming negotiations with his UK counterpart David Frost.
The European Union will need to move in negotiations but it is in the interests of both Britain and the EU to get a trade deal, according to the UK finance ministry.
"The fundamentals remain the same, it is in both sides' interest to have a deal," Steve Barclay, Chief Secretary to the Treasury, told Sky News.
"Whether there is a deal is not simply down to the actions of the Prime Minister. It needs the EU to move," he said.
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For months the talks have been deadlocked on the issues of fishing rights, the "level playing field" to ensure neither side can unfairly compete with the other on environmental standards, workers' rights or state subsidies, and the legal mechanisms to govern any deal.
Mr Barnier said the "next few days" are important if a deal is to be in place for 1 January.
"It is our responsibility to give the talks every chance of success," he said.
"Never before has such a comprehensive agreement (trade, energy, fisheries, transport, police and judicial co-operation etc) been negotiated so transparently and in such little time."
A spokesman for the grouping of EU ambassadors said there is "full support for the resilient and persistent" negotiating team led by Mr Barnier.
The UK's current trading arrangements with the EU expire at the end of the month, meaning any new deal would have to be in place by 1 January.
If not, tariffs and quotas will apply and bureaucracy will increase, causing further damage to the UK economy which has already ravaged by coronavirus.
Additional reporting Reuters