The Taoiseach says efforts are being made to arrange another meeting with the British Prime Minister ahead of a European Council Summit in two weeks time.
Leo Varadkar says he believes a Brexit deal can still be struck and that Friday would be a reasonable deadline.
Mr Varadkar says time is tight, as it is not acceptable to expect heads of Government to sign off on something, they only see the night before or a few days before.
"There are a lot of countries - including our own - where there is a degree of Parliamentary scrutiny so timelines are tight," said Mr Varadkar.
"It's always possible to find an extra 24 hours or 48 hours but it is not the case that you can negotiate an international treaty at a council meeting in Brussels.
"Sometimes we might be able to come to an agreement."
Mr Varadkar said people across the EU accept a Brexit extension would be better than no deal.
According to Mr Varadkar, the UK has not proposed further solutions to break the deadlock and problems remain around the issues of consent and the prospect of customs checks.
"The current position as of today is that the European Union including Ireland doesn't feel that the proposals put forward by Prime Minister Johnson yet form the basis for deeper negotiations.
"But there is plenty of time for the UK government to put forward further proposals and we are in the process of trying to arrange a meeting between myself and Prime Minister Johnson next week."