Having a post-Brexit trade agreement concluded within 12 months is "wildly beyond credibility", according to Minister for Agriculture, Food and Marine, Michael Creed.
Speaking on RTÉ's The Week in Politics, he said it should be clearly indicated by British Prime Minister Boris Johnson by the end of June that they want an extension.
He said his optimistic interpretation following the UK election is that the Tories have moved to the centre ground, and "borrowed Labour voters".
"The likelihood is that the majority will change the dynamic in the House of Commons. And that the ERG will become more marginalised in that endeavour."
However, he said first we have to wait and see as there are deadlines, the first one being 31 January, which Mr Johnson has said is the date that the UK will leave the European Union.
Mr Creed said he thinks that having won over Labour voters, Mr Johnson is going to be conscious of keeping that platform together and building a more consensus type approach.
The minister also said "the bread and butter of the economic issues" is now the focus of the Brexit debate.
He said the agri-food and fisheries sectors are hugely important to the rural economy and he thinks the fisheries issue in particular could be significant regarding talks on a future trading relationship.aid.
"There is no constituency in the UK that has had its expectations raised higher than the fishing communities.
"And in terms of here, a third of our endeavour is in UK territorial waters. Were they to try and pursue a hard Brexit, it would have a catastrophic impact for us. And for the UK."
He said it is not just Ireland airing its concerns, but right across the EU.
"It is now 27 member states. We have forged an alliance of all like-minded states on the fisheries side for example and clearly prosecuted that argument into the Barnier task force so that the outcome on fisheries is inextricably linked with the trade negotiations, and not isolated on a silo basis.
"And that is really important for our fishing communities."
It comes as UK cabinet minister Michael Gove said the top priority of Boris Johnson's government is to leave the European Union on 31 January.
Mr Gove told Sky News that parliament would have the opportunity to vote on the EU Withdrawal Bill in relatively short order.
The government's top domestic priority, he said, would be shoring up the public health service.
Mr Gove ruled out holding another referendum on Scottish independence, despite the SNP increasing the number of seats in the Commons.
He said the Tories would "absolutely" not hold another public vote on the matter during the course of the Parliament regardless of how Scotland votes in the 2021 Holyrood election.
Mr Gove told Sky's Sophie Ridge on Sunday: "We were told in 2014 that would be a choice for a generation, we are not going to have an independence referendum on Scotland."
With the Tories having won Labour voters across the north of England and the midlands, Mr Gove stressed the need to deliver for its new supporters.
"We need to make sure that economic opportunity is more equally spread across the country," he said.