The Prime Minister is to travel to Dublin on Monday for his first official meeting with the Irish Premier.
Boris Johnson and Leo Varadkar will meet in the city for talks on Brexit, restoring institutions in Northern Ireland and concerns over no-deal.
Speaking on Sunday, ahead of the meeting, Mr Varadkar said he did not expect a breakthrough.
"I don't think the meeting tomorrow is a high stakes meeting, as I don't anticipate a big breakthrough tomorrow, if we come to an agreement that agreement will happen in October at the EU summit," Mr Varadkar said.
The Irish Government has consistently stressed that negotiations on Brexit will only take place between the UK and the EU27, and the meeting will be about "sharing ideas" rather than negotiating bilaterally on the UK leaving the EU.
"It will be an opportunity to get to know each other a little bit better, to see if there is common ground, I'm sure there will be," Mr Varadkar added.
There has been much public interest in the meeting, with former secretary of state for Northern Ireland, and Labour MP Peter Mandelson, speaking on Ireland's national broadcaster RTE telling the Taoiseach: "not to be taken in" and "don't be conned" by Mr Johnson.
Sir Keir Starmer, Labour's shadow Brexit secretary, speaking ahead of the meeting released a statement saying that the British government intends to "backtrack on solemn commitments made to the people of Northern Ireland".
"Those commitments were the foundation of an agreement with the EU that would protect the peace process and avoid a hard border in Northern Ireland," Mr Starmer said.
"When Boris Johnson meets the Irish Prime Minister, he must make absolutely clear there will be no rowing back and the Government will not take the negotiations down such a reckless path."