"Talks with the DUP have been progressing well, and there is broad agreement on the principles of the Queen's speech", the source said, referring to the government's legislative program.
Northern Ireland has been without a powersharing executive since March and without a first and deputy first minister since January, after Sinn Fein collapsed the administration amid faltering trust and relations with the DUP.
Ms Foster said the talks deadline remained "realistic".
"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.
"We want to get back to an executive that has all the parties around the table to collectively take decisions".
"I think it is all very doable".
Sinn Fein's Stormont leader Michelle O'Neill also sat down with the Taoiseach yesterday, a series of meetings partymembers Gerry Adams, Mary Lou McDonald and Michelle Gildernew also attended.
UK Labour leader Jeremy Corbyn
Major said taking the unionists party into a British coalition government could imperil the accords.
Speaking to reporters in Dublin, Foster, whose Democratic Unionist Party (DUP) is in talks with Theresa May's Conservatives after they failed to win a majority in the election, said: "We want to see a Brexit that works for everybody, not just in Northern Ireland from my perspective, but of course in the Republic of Ireland as well, so it is about a sensible Brexit".
Foster yesterday dismissed suggestions her deal with Theresa May has undermined the Peace Process in the North.
"There is an irony to being lectured by some about our role in the national government of the United Kingdom when Sinn Fein want to be in government here in the Republic of Ireland", she said.
He said she wanted to limit the ability of those with civil partnerships in Northern Ireland to convert them into marriages in Scotland.
"What would happen then?"
May faces the task of satisfying both the pro-European and eurosceptic factions of her party, keeping Northern Ireland calm and negotiating a divorce with 27 other European Union members whose combined economic might is more than five times that of Britain.
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Meanwhile, the other half of Dolce & Gabbana returned fire with a scathing comment on her Instagram post . "We believe in trying something new everyday!".