The European Union agreed on Friday to enter intense talks with Britain to try to break the deadlock over Brexit, lifting financial markets with a sign that a deal could be done before the Halloween deadline.
Mr Varadkar has reiterated time and again that there will be no hard border in Ireland- the offer of a deal from Mr Johnson last week was rejected on the grounds that there would be checks on goods-vehicles crossing between Northern Ireland and the Republic.
A flurry of activity has brought the fraught bargaining process to a new level as Britain's scheduled departure date of October 31 grows ever closer, but it is still uncertain whether the two sides can make a breakthrough before then. They said the two sides will intensify talks to that aim.
Negotiators have been given the green light for talks to enter the so-called "tunnel" phase - diplomatic jargon for talks continuing in secret between a small group of negotiators in complete secrecy - with a view to presenting a deal ahead of the European Union summit on 17 and 18 October.
In a statement on Friday, Mrs Foster said the party, whose support will be key to getting a Brexit deal through Parliament, would only back a deal that is in Northern Ireland's "long-term economic and constitutional interests".
The EU's chief negotiator Michel Barnier is now meeting with Britain's Brexit minister Stephen Barclay in Brussels.
"We need vigilance, determination and patience", Barnier told reporters on his way to debrief European Union ambassadors and Parliament's Brexit group. The Prime Minister is very mindful of that.
After the Irish prime minister (or "taoiseach") Leo Varadkar suggested that a deal could still be done on-time following one-on-one talks with Prime Minister Johnson and a meeting between Barnier and Britain's Brexit Secretary Stephen Barclay, however, the word has gone out that "tunnel" negotiations may (or may not) be on the cards - although few reporters have elaborated on what this actually means.
To get a deal done, he must also sell any deal to the British parliament, which he suspended unlawfully last month and where his Conservative Party has no majority.
The pound's rise since Thursday is the biggest two-day gain since before the Brexit vote in 2016.
One way to do that could be to extend the October 31 deadline so that negotiators have more time to work things out in legally-binding detail.