"It continues and when the deal is done, it will be done", a senior source in the Conservative Party said on Thursday. Foster also said a deal on power-sharing in Northern Ireland is "very likely" this month, according to RTÉ.
The prime minister has been holding talks with Northern Ireland's Democratic Unionist Party, keen to get the backing of their 10 lawmakers in parliament to help her pass laws and govern as Britain starts talks to leave the European Union.
The DUP, under Mrs Foster, is close to striking a deal with the Conservatives that would allow a beleaguered Theresa May to form a minority government in London.
"With ten members elected to Parliament we will make sure both the farming and fishing industries will be discussed to the benefit of both in Westminster", Shannon said.
In 2011, Fine Gael appointed Mr Varadkar as the minister for transport, tourism and sport - and then health minister.
Mr Dodds said that the speech was "not relevant" to their negotiations.
Colum Eastwood, leader of the SDLP, Northern Ireland's second-largest Irish nationalist party, said his party had a "positive" meeting with the prime minister over her efforts to come up with a deal with the DUP.
No deal yet between UK Conservatives and DUP to back PM May
After House Speaker John Bercow was re-elected without challenge, a chastened May quipped: "At least someone got a landslide". However, a deal with the DUP also risks destabilising Northern Ireland by increasing the influence of pro-British unionists.
More recently he has overseen Ireland's welfare system.
Speaking to reporters after the meeting, Foster, whose party has been locked in talks with the U.K. Conservatives since Theresa May lost her majority in parliament in last week's election, said she hoped Brexit would benefit the Republic of Ireland and the United Kingdom, Reuters reported. The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week, as well as change Britain's entire approach to its EU withdrawal.
There are questions over how long Foster, who was the minister with responsibility for the scheme from its inception in 2012 until 2015 - knew the initiative was flawed.
Sinn Fein's Stormont leader Michelle O'Neill said: "I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements".
Ireland has a key role in the arrangements and structures set out in the Good Friday Agreement that has led to a period of peace in the trouble-torn region.
"An agreement to restore devolved power-sharing government in Stormont must be reached by the 29 June deadline".
But critics argue such a deal could undermine the peace process.