Tánaiste and Minister for Foreign Affairs Simon Coveney has suggested that a Brexit deal may not be possible at the EU summit in Brussels this week.
He said talks could drift into next week, but added there was goodwill and determination on both sides to get a deal done.
Speaking in Luxembourg, Mr Coveney said: "I think it's too early to say, even though we're only a few days away from the summit. It's too early to say whether it's possible to get a breakthrough this week or whether it will move into next week."
Mr Coveney said both teams of negotiators should be allowed to continue their work in a "confidential and intensive" way.
He said there were still significant gaps to close, and what both sides were trying to achieve was highly complex.
"What they're attempting to do here is to write a legal text for an international treaty, that is a Withdrawal Agreement," he said.
"That means it's got to be watertight, it's got to stand up to full scrutiny and legal challenge potentially, and what they're trying to do is complicated.
"They're trying to put in place an arrangement that is Northern Ireland-specific, that protects UK interests and EU interests, in a way that's quite complex. So we need to give negotiating teams space to do that, I think there is goodwill and a political determination to get this done."
He told reporters: "The negotiations have come from an agreement from the Taoiseach and PM last week, that they could see a pathway to a possible deal.
"They can see an approach here that they believe can work and that approach has then been taken forward by two negotiating teams, they've intensified their focus on trying to make that work."
Michel Barnier, the EU's chief negotiator, is expected to indicate later tonight whether he believes both teams can conclude a deal at this week's summit.
Sources suggest both sides are far apart on customs, and there has been strong pushback on the UK's proposals for a customs partnership that would see Northern Ireland be part of the UK's customs territory, but applying EU rules and procedures on tariffs.
It is understood the European Commission is trying to edge the UK back to the original Northern Ireland-only backstop as a clearer and more legally operable solution.
Mr Coveney said the European Commission Task Force was capable of drafting a text if that were possible.
"They are very smart people who can put language together that can work. The UK of course have got to contribute to that too," he said.
"It is being left very late in the day but we shouldn't write off this summit as a potential opportunity for agreement."
Customs 'front and centre' of talks
Vice President of European Parliament, Fine Gael MEP Mairead McGuinness, said she does not believe that Brexit negotiations can be completed by Thursday, but it is a good sign that talks have not broken down.
Speaking on RTÉ's Today with Sean O'Rourke, Ms McGuinness said the customs issue is "front and centre of the negotiations".
She said something cannot be accepted in the short term that will cause problems in the medium and long term.
Meanwhile, the President of Sinn Féin has said she welcomed the fact it appears that a real substantial Brexit negotiation is taking place.
However, Mary Lou McDonald added she was not in a position to judge whether the negotiations were real or not, because she is not party to them.
Speaking on RTÉ's Morning Ireland, she added that we will only be able to judge if the negotiations are real "if and when we see the colour of London's money and what they have actually put on the table".
Ms McDonald spoke to British Prime Minister Boris Johnson yesterday and said he informed her that he wishes to reach a deal.
In addition, Mr Johnson said he understands there cannot be a customs border on the island of Ireland and that he understands and supports the Good Friday Agreement.
However, she said that he did not say how he "could square the circle".
Ms McDonald said she did not fully understand the concept of seeking the consent of the Northern Ireland assembly, but reiterated that Sinn Féin will not allow for any form of veto for unionism to hold the island of Ireland to ransom.