"We want the negotiations to move on to phase two so we can talk about our future trade relationship".
Right now, the U.K.'s government is being propped up by a small party from Northern Ireland.
"We are looking for significantly more clarity than we now have from the British negotiating team", Coveney told parliament in Dublin, adding that "constructive ambiguity" from Britain would not suffice.
MPs have said a return of border checks between the Republic of Ireland and the north seems "inevitable" after Britain leaves the European Union.
She said her party supports the continuance of the Common Travel Area allowing people to move freely between the North and the Republic.
A breakthrough on the issue of the border between Ireland and Northern Ireland after Britain leaves the European Union is "doable" before the EU summit on December 14, Irish Foreign Minister Simon Coveney said on Friday.
MPs: Technology can not prevent the return of Irish border checks
But any attempt at a solution will have to convince Northern Ireland's pro-Brexit Democratic Unionist Party, whose 10 members of parliament are propping up May's government.
With significant progress on the financial settlement and citizen rights, a deal on the Irish border would pave the way for Brussels to offer British Prime Minister Theresa May a transition deal as early as January.
The EU will decide in mid-December whether there has been sufficient progress in Brexit negotiations to consider moving the talks to a further stage where future relations between the United Kingdom and the bloc are discussed.
I view the so-called problem of the border between Northern Ireland and the Republic of Ireland nothing more than the Republic of Ireland using an opportune moment to capitalise on Britain's/Brexit's refusal to accept the European Union single market and customs union.
Efforts to reach a deal are to intensify with Taoiseach Leo Varadkar to hold talks with European Council President Donald Tusk in Dublin tomorrow.