Varadkar said earlier this week that he still hopes the UK will pull back from its plans to leave the EU single market and customs union, citing this as the best solution for avoiding a border on the island of Ireland or between Ireland and Britain.
Asked if he thought there was a chance Brexit would not happen, he said, "Well I still hope that it won't happen. Brexit is a British policy, not an Irish one.
"It's the UK that's decided to leave and, as far as I'm concerned when it comes to my work in Brussels, working with other European prime ministers and presidents, it's part of my remit to keep the door open, not just to the EU but also to the single market and also to the customs union should they decide to go down that route.
"That, I think, would be the best outcome for Ireland and Northern Ireland and Britain."
Arlene Foster, the Democratic Unionist party leader, has now accused the Taoiseach of disrespecting the will of the British people by publicly admitting that he hoped Brexit would never happen.
She said his comments were unhelpful.
Elsewhere, Maltese Prime Minister Joseph Muscat has said that he believes that Brexit will not happen.
His comments come in an interview he gave to Dutch newspaper De Volkskrant.
"For the first time, I'm starting to believe that Brexit will not happen. I am seeing hopeful signs that indicate things will change," Muscat told the newspaper.
"It would be good if a political leader in the UK stands up and is courageous enough to address this new situation. Someone who says: let's put the Brexit end-deal to a popular vote," he said.
Muscat has branded Brexit "a disastrous creature" which the European Union should have seen coming.
Meanwhile, the EU Brexit negotiator Michel Barnier has reportedly told EU diplomats he and his team will work through August, including on 15 August Belgian public holiday, at the request of Commission President Jean-Claude Juncker, as both Brussels and London want to speed up talks.
According to press reports, four diplomats who attended a recent Barnier briefing said he wants to up the pace of negotiations and avoid British reluctance to talk about a financial settlement becoming a problem at the October EU leaders summit.
Sources have denied an earlier report in the Daily Telegraph newspaper that talks "will be delayed for two months because of the UK's refusal to engage with Brussels."