Coveney recalled that the current composition of the London Parliament, where May has no majority, has always shown that the only way to complete Brexit is through collaboration between the Conservative Party and the Labour Party, which is led by Jeremy Corbyn, a democratic socialist who has been leading the opposition since 2015.
May said Tuesday that she plans to request a further extension of the Brexit to Brussels to negotiate with Corbyn a joint plan that will ensure the House of Commons' support.
"There are actually a number of areas we agree on in relation to Brexit," Prime Minister May told Parliament and added that "what we want to do now is to find a way forward that can command the support of this House and deliver on Brexit."
Should May and Corbyn design a new roadmap, the EU could accept a Brexit extension at the extraordinary summit next April 10, that is to say, two days before the date set for U.K.'s departure.
The Labour Party is, however, far from united. Corbyn said that the Brexit deal should include a customs union with the E.U., consumer protections, environmental standards and workers’ rights.
Many of its supporters want the left-wing party to throw its weight behind a second referendum. But some Labour lawmakers, who represent areas that voted strongly to leave the EU, not only reject this but also fear that a "Soft Brexit" would be seen as a betrayal.
Corbyn said any agreement with May, who has promised to resign if a Brexit deal is passed, must be set in law to guarantee that it could not be changed by any successor.
Although a Brexit extension must be have the 27 EU countries' unanimous support, May's proposal momentarily dispels the possibility of a "Wild Brexit," according to Coveney, as reported by the Irish public media RTE.
In his opinion, all of May's options are "difficult", but she has "done everything possible" to gain the support of the most Eurosceptic wing of her party and that of her government partners, the Northern Irish Democratic Unionist Party (DUP), which rejected Wednesday her approach to Corbyn.
Whether or not the Conservative and Labour parties reach a deal by the end of the week is something that "we will have to wait and see," Corvey said, adding that Ireland must still prepare for a no-deal scenario, although he warned that his country will not accept a physical infrastructure on the border.