Tániaste Simon Coveney has said that optimism that has been reported in recent days in relation to the Brexit negotiations is "probably not well founded".
Speaking on RTÉ’s News at One programme, he said people should be realistic about time frames.
However, he said he hoped that negotiators would be able to make a "big step forward" next week.
"The negotiating teams ... will hopefully have some political recommendations to feed political leaders early next week," he said.
EU leaders are meeting at the end of next week for a two-day summit in Brussels.
Meanwhile, the head of the European Commission Jean-Claude Juncker has said that "substantial progress" was needed in Brexit negotiations, particularly in relation to the issue of the Irish border.
"I want to believe that we will be able to find a deal with our British friends between the European Council meeting next week and the possible one in November," he told French newspaper Le Monde.
"We therefore need substantial progress, which we should be able to see next week," Mr Juncker added, referring to a meeting of EU leaders in Brussels where Brexit is set to top the agenda.
Earlier, the EU’s Brexit negotiator said he had a "constructive meeting" in Poland over Brexit.
In a post on Twitter, Michel Barnier said "We continue our constant dialogue with EU27 member states."
Mr Barnier has been touring EU capitals for months and visited Warsaw today as Brexit talks have entered a crunch period.
Poland, which has about a million citizens living in Britain, has at times sounded more conciliatory toward British demands than other member states.
EU27 consultations in Warsaw. Constructive meetings this morning with PM @MorawieckiM and Minister for EU affairs Konrad #Szymanski. We continue our constant dialogue with EU27 Member States. #Brexit pic.twitter.com/g7kSaUFiAx— Michel Barnier (@MichelBarnier) October 12, 2018
Meanwhile, the DUP warned that British Prime Minster Theresa May knows the consequences if she walks away from her Brexit promise to unionists.
At a party gathering in Mid-Ulster where members were briefed on the Brexit process, Brexit spokesman Sammy Wilson urged Mrs May to show EU negotiators "the door".
He said: "She has declared herself to be a unionist, she has repeated that time and time again, she knows the consequences if she walks away from that promise, not just for Northern Ireland because of course she will open a Pandora's box in Scotland as well.
"I am sure the Prime Minister is well aware of the grave responsibility which lies on her shoulders."
Additional reporting PA