Prime Minister Andy Burnham alluded to the potential of the UK rejoining the EU and many are wondering what that could mean for Britain, Ireland and the future of the EU relationship.
Former Taoiseach Leo Varadkar joined Ciara Doherty on The Pat Kenny Show and shared his opinions on the UK potentially rejoining the EU.
Prime Minister Andy Burnham spoke to the BBC's Chris Mason about the potential plans to hold another election, and when asked specifically about it being included in a future Labour manifesto, he replied: "Yes, things are possible. I think where we are isn't good enough."
When it was pointed out by the host that if their return is made too easy, then it might encourage other countries to give their own Brexit a go, to which Mr Varadkar agreed is a "risk".
He explained: "That's a genuine risk. Like one of the reasons why the treaties made it so hard to leave was so that countries wouldn't leave. And one of the reasons why the UK could never get a good deal would be because if they did get a good deal, then everybody else would seek one too.
"Actually one of the interesting effects of Brexit is the nationalist parties of the far right and the far left that had previously advocated their country leaving, they kind of dropped that.
"There's a risk if it's too easy to rejoin, that there's a risk that countries might take a chance on it. But I think in balance, the value of having the UK back in is such a positive for all of us.
"I think maybe it can have a demonstration effect that a country left and went through all that fuss and now has to go through all the fuss of coming back. It's like leaving a job and then going back to it, you know?"
So how does he think it could work?
He continued: "I think what they could do is saying that they want to come back in and they want a new partnership. And, you know, certainly from Spain, from Germany and to lesser extent from France, the response has been very positive.
"The French have pointed out [Macron] very correctly that there can't be cherry picking. You can't just pick the good bits of membership and not the obligations.
!But I think it would be possible to construct something that would work for them and might help to light a fire under the EU itself, because we haven't had significant change as to how the EU works since the Lisbon Treaty. That's a long time ago.
"We don't need another referendum or anything, but there are changes that could be made to reform the EU, to make it better. And this might be the opportunity to do it."
Minister Thomas Byrne, who is the Minister of State for European Affairs and Defence, was also asked if he and the EU are ready to "welcome the UK back with open arms," to which he said there were two answers to that question.
He explained: "One is as Ireland and the other is as Irish Presidency of the European Union at the moment.
"I have to be very, very careful with anything I say because, obviously, I have to represent all of the member states and big questions like that at the moment while we're at presidency.
"But look, in all seriousness, there is a process in front of us in the coming weeks, actually, to get a summit achieved and to get agreement on really specific things that will benefit Great Britain, will benefit us, will benefit the EU on import and export of food and plant products on the emissions trading scheme, on the youth experience scheme.
"So that's real work that we're doing in the presidency at the moment. Probably on the 1st of January, I can answer that other question with a straight face when we're finished at the presidency.
"But as presidency, we're really preparing the ground for some of this work that will actually make a difference."
Main image: UK and EU flags, Picture by: PA Wire/PA Images