Former taoisigh Bertie Ahern and John Bruton have said they believe that a second Brexit referendum is the only way forward.
Speaking on RTÉ’s The Week In Politics, Mr Ahern described the Brexit situation as "a mess", and said that he would love to see another referendum.
However, he said that there are indications that progress is continuing in the ongoing negotiations, but probably not enough to warrant an EU Council meeting this month.
Mr Ahern said that caution must be exercised in relation to the talks between Europe and Britain.
He warned that if Britain got its way and got to the point of the future relationship they will say the backstop does not matter.
He said Ireland must be very careful as there is no guarantee that the backstop will not be needed in the future relationship.
He said that British Prime Minister Theresa May and her legal team have been "trying to push everything together".
"They have been trying to push the Article 50, the Withdrawal Agreement and the future relationship together, and they are still at it.
"And I think they still will be trying to build on this, not a Chequers deal, but push the three of them together, and I think that we have to be very careful."
Mr Bruton said he thinks that a second Brexit referendum is "probably going to be the only way out for Theresa May".
Speaking on the same programme, he said: "She'll find that she doesn't have the majority to put the agreement through and she will then say, rather than having a general election, lets have a referendum, with this as an option or staying in the EU."
Asked what happens with the border if there is a "crash out" Brexit, Mr Ahern said Ireland would have to negotiate with the EU27 on how it would check out goods.
Mr Bruton said however that could be quite difficult if Britain is not being cooperative because of the resentment it feels.
Mr Ahern said the constitutional position of Northern Ireland does not arise in Brexit in his view.
He said it was settled in the Good Friday Agreement and the people of Northern Ireland will decide whether they are British or Irish.
Meanwhile, Minister for Justice Charlie Flanagan has said that the Irish Government does not underestimate the challenge ahead in reaching a Brexit deal, but he remains confident that a resolution can be worked out.
Speaking in London, where he will represent the Government at an event to commemorate the Armistice in Westminster Abbey this evening, Mr Flanagan said negotiations are at a sensitive and delicate phase.
The Minister said he saw no evidence that the EU wanted to inflict any trauma or suffering on the UK in any deal. He says there is still confidence that a deal can be reached in the coming weeks.
Mr Flanagan's comments come amid reports in the British press that a proposal from the UK about how and when the UK could exit any Northern Ireland backstop has been rejected by the EU.
The Sunday Times reports that Mrs May had suggested an independent panel would be established to adjudicate on when the backstop could be left.
It is understood the EU rejected this, saying that any such decision should be made by the European Court of Justice.
Additional reporting: Fiona Mitchell