Taoiseach Leo Varadkar has said he thinks a Brexit deal can be done by November.
The Irish border is the most vexed issue still facing UK and EU negotiators.
The Republic’s premier warned the damage caused by talks failure to Britain and Ireland would be “immense”.
A special meeting of European leaders in Brussels has been mooted for November if the two sides are close to reaching agreement.
Mr Varadkar said: “I do think we’ll get there.
“I think we’ll get there in November because nobody wants us to end up with a no-deal scenario because the damage for the UK would be immense.
“The damage for Ireland would also be immense and it would have a serious impact on other countries like Belgium, Holland, and France and Denmark.
“So I believe we will get there in November but we are in unchartered territory.”
The EU has interpreted a backstop, agreed in principle between the UK and Europe in December, to mean that, in the absence of a trade deal, Northern Ireland would continue to follow EU rules relating to commerce and thus prevent the imposition of a hard Irish land border.