The Minister for Foreign Affairs does not expect the EU and Britain to agree a deal on the Northern Ireland Protocol by Christmas.
But Simon Coveney thinks it may be possible to sort out some problem areas, notably on the issue of the supply of medicines from Britain to Northern Ireland.
He is on a visit to London today for meetings with both the UK Brexit minster David Frost and the British Irish Intergovernmental Council.
Mr Coveney told RTÉ News: "I don't think there will be a full deal on all issues related to the protocol for Christmas. But I think some things can be agreed this side of Christmas, hopefully, like giving certainty to people in Northern Ireland in terms of the supply of medicines from Great Britain into Northern Ireland."
The EU negotiator, Commission vice President Maros Sefcovic, has tabled a proposal to change EU law to allow certain medicines authorised in Britain to be sold in Northern Ireland, to avoid changes brought about by Brexit causing a shortage or non-availability of some medicines.
"If we could get that agreed before Christmas it would be very useful," Mr Coveney said. "It's been difficult to make progress, but I think there has been some progress."
He said it was "important to encourage both sides to try to find landing zones and compromise positions on important issues in particular around the the guarantee of supply of medicines into Northern Ireland from Britain".
This was something that "I know both teams have been trying to resolve in recent weeks and hopefully we can make progress", Mr Coveney said.
He added that while the Irish government is very close to Maros Sefcovic and his team, it was important to travel to London to try and understand more about the British position.
Tomorrow, Mr Coveney and Minister for Justice, Helen McEntee, will meet the Northern Ireland Secretary of State, Brandon Lewis, and Northern Ireland Office minster Conor Burns in a formal meeting of the British Irish Intergovernmental Council.
As well as the political and security situation in Northern Ireland, the ministers will discuss the British proposals on dealing with the legacy of the Troubles.
This includes a UK government proposal to introduce a statute of limitations that would effectively end all prosecutions related to The Troubles up until the signing of the Good Friday Agreement.
Mr Coveney said: "We don't support that approach. No party in Northern Ireland does. And none of the victims groups do either. But we are, as a Government, of course willing to work with the British government in partnership to try to find a basis for consensus.
"Don't forget, back in 2015, we agreed how to deal with legacy capacity in some detail in the Stormont House agreement. The British government wants to move away from that agreement.
"We are open to talking to them about that, but it's got to be done on the basis of consensus and agreement with politicians, and most importantly victims groups in Northern Ireland."
He added: "I certainly hope that the British government is not going to move ahead and act unilaterally against the wishes of everybody else who has been part of this process, who want to see a different approach ..."
Earlier, French President Emmanuel Macron said the Northern Ireland Protocol was a "question of war and peace for Ireland" and an existential question for Europeans.
Speaking to the EU Committee of the Regions, President Macron said: "The Protocol is of existential importance for Europe not to compromise when it comes to our single market, the integrity of that, otherwise there are no longer any rules at the borders.
"It's a question of war and peace for Ireland. So we should avoid any temptation to be less than serious.
"And so I think that we should not play with this issue, but it is an issue that we will deal with in Europe in a united way as from day one whether it's fisheries, or the Irish agreements, or migration.
"All of these are issues between the EU and the United Kingdom."
Mr Macron - who has clashed in recent weeks with the British prime minister Boris Johnson over migration across the English Channel and fisheries - said the Protocol was fundamentally about how to reconcile the Good Friday Agreement and the integrity of the EU's single market.
"That's the debate we’ve been having for many months with our British friends," he said.
Also today, European Commission vice president Maros Sefcovic urged the UK to "reciprocate" in talks over the Northern Ireland Protocol.
Mr Sefcovic insisted the benefits of the protocol are "immense", offering Northern Ireland access to EU and UK markets.
He was speaking as he appeared remotely before the Northern Ireland Assembly's Executive Committee.
Mr Sefcovic said he wanted to "reaffirm the EU's overarching objective to establish a positive and stable relationship with the United Kingdom".
"We have been showing flexibility and creativity in finding solutions within the framework of the protocol," he added.
The protocol is "not perfect but it is the best response to the UK's decision to withdraw from EU and the form of Brexit the [UK] government has chosen".
Mr Sefcovic said political and technical discussions between the EU and UK are continuing, and he will speak to the UK's chief Brexit negotiator David Frost on Friday.
"I can assure you that I am sparing no efforts to reach solutions," he told MLAs.
"We will remain calm and constructive but also firm. The EU stands united, our commitment to the Good Friday/Belfast Agreement is absolute, the key prerequisite for this is the avoidance of a hard border on the island of Ireland."
Additional reporting: Tony Connelly, PA