Update: Former Taoiseach John Bruton has said he believes that a no-deal Brexit is the most likely outcome.
It comes as a crunch meeting over the Brexit deadlock is expected between Taoiseach Leo Varadkar and British prime minister Boris Johnson in the coming weeks.
Speaking to RTÉ, he said the current state of Anglo-Irish relations is "not good", and the two nations are "in profound disagreement".
The former Fine Gael leader urged the Taoiseach to "stay calm and quiet and wait" and said that he has the full support of the European Union.
Mr Bruton said: "At the end of the day Britain has to have ownership of the solution, but if they have not come forward with any ideas, they are not going to have ownership of it. They must be encouraged to confront these ideas themselves."
There has been no breakthrough in the Brexit deadlock between Dublin and London in efforts to arrange talks between Taoiseach Leo Varadkar and British prime minister Boris Johnson.
Despite reports that Mr Johnson has accepted an offer from Mr Varadkar to meet and resolve issues, officials have indicated no arrangements or progress has been made or date agreed for any such meeting.
There had been hope the two leaders could meet and discuss Brexit ahead of a G7 summit in two weeks time.
But any such meeting is now more likely to take place in early September.
The Sunday Telegraph reported today that dates were being discussed and that the new British prime minister had now “accepted” the offer.
Mr Johnson wants to rip up the Withdrawal Agreement, to drop the backstop that prevents a new border and is intent on crashing Britain out of the EU at the end of October if no deal is agreed.
Government sources said there was nothing agreed on a meeting and no indication of any major development.
A spokesperson for Mr Varadkar told the Irish Examiner this morning: “The Taoiseach has invited the British Prime Minister to Dublin for talks on Northern Ireland and Brexit.
"Their offices are in contact to agree a date for these talks in the coming weeks.
“Such a meeting would give both sides an opportunity to gain a better understanding of their respective positions.
"As has repeatedly been made clear, the Withdrawal Agreement and the backstop are not up for negotiation.
"Any discussions on changes to the political declaration would occur be between the UK and the EU.”
Mr Johnson is set to meet French leader Emmanuel Macron, German chancellor Angela Merkel and US president Donald Trump in Biarritz in two week's time at a G7 summit.
Scheduling any meeting between him and Mr Varadkar before then is unlikely, sources have said.
Instead, a date in early September may be preferable.
But this could also be problematic if any snap general election is called in Britain.