The Taoiseach expects to meet British prime minister Boris Johnson in New York next week as the Brexit talks remain in deadlock.
Both leaders were in contact this morning and now hope to speak in person on the fringes of a special UN Summit on Climate Action in New York which begins on Monday.
At the National Ploughing Championships in Fenagh, Co Carlow, Mr Varadkar said a Brexit deal would have to be hammered out in advance of any EU Council meeting as it wouldn't happen "at 5am with 27 Prime Ministers and their teams trying to write up a treaty".
He was responding to comments made by Finnish prime minister Antti Rinne who said Boris Johnson has until the end of the month to set out his Brexit plans to the EU.
While Mr Varadkar said no deadlines have been set by either the Irish government or European Union, he stressed there is now no time to waste on reaching an agreement.
"I think what Chancellor Merkel and also the Finnish prime minister are saying is that there is a European summit coming up on October 17.
"That's the opportunity to come to an agreement. But the way Europe works is that it really has to be teed up before the meeting.
"It's not going to happen at 5am with 27 Prime Ministers and their teams trying to write up a treaty.
"That's not the way these things are done.
The Taoiseach moved to allay fears over medicine shortages and food supplies in the case of a no-deal and said he is confident there will not be difficulties in these areas.
"There will absolutely be food on the shelves, some brands particularly British brands may not be available, but there will be food on the shelves. People don't need to be concerned about that.
He added: "The two countries that are going to be worst affected in the event of a no-deal are going to be Britain and Ireland. Most countries on the continent will barely be affected at all.
"So it is in the interest of the United Kingdom to put forward proposals that allow them to leave the European Union in an orderly fashion that minimises the damage to their country, their economy and ours."