The Taoiseach says European leaders are "confused and puzzled" over the British stance on the customs union
The Minister for Foreign Affairs has said that Ireland's special relationship with Britain allows officials from both islands host "honest and blunt" conversations on Brexit.
Minister Coveney met with the Northern Ireland Secretary James Brokenshire in Dublin this evening.
The two men discussed the political deadlock over power sharing in the north - as well as the ongoing issues surrounding Brexit and the Irish border.
Mr Brokenshire reportedly confirmed during the meeting that there is no possibility the UK remaining within the customs union following Brexit - insisting that to do so would prevent lawmakers from negotiating international trade deals.
It comes after the Taoiseach Leo Varadkar said European leaders are "confused and puzzled" over the British stance on trade.
He said Britain appears to want to leave the customs union while keeping the benefits of the customs union and single market.
He said the two positions do not tally and called greater clarity on the issue.
Speaking to reporters ahead of this evening's meeting Minister Coveney said: "Our relationship with the British government and with the UK generally is such that of course we need to have honest and quite blunt discussions in terms of what we think will fly and what won't."
"We will be having those discussions," he said.
"I have had a number of telephone conversations with the Secretary of State over the summer and this is an opportunity now to build on that interaction."
Following the meeting, Minister Coveney said he raised the government's continuing concerns over the impact of Brexit on Northern Ireland.
He noted that the issues can only be resolved through the ongoing Brexit negotiations.
“I underlined that protecting the peace process and maintaining the gains of the Good Friday Agreement is crucial and that this shared responsibility must be fully upheld in the negotiations between the European Union and the UK.”
He also reaffirmed both government's determination to see power sharing restored in the north.
"Both Governments will leave no stone unturned in the weeks ahead in supporting the parties to achieve that essential objective,” he said.
Earlier, Mr Brokenshire met with the Minister for Justice Charlie Flanagan and the Tánaiste Frances Fitzgerald.
A spokesperson for Minister Flanagan said he had taken the opportunity to acknowledge the publication of the British government's position papers on customs arrangements and the Irish border following Brexit.
He welcomed the emphasis on maintaining the Common travel Area, protecting the Good Friday Agreement and avoiding a hard border in Ireland.
In a statement, the minister said that paramilitary groups opposed to peace "remain the greatest security threat on the island of Ireland."
"The Secretary of State and I discussed our ongoing cooperation on combating that threat," he said.
"The Gardaí and the PSNI continue to work together effectively to tackle these groups and their associated criminality.
"The Fresh Start Agreement has a particular emphasis on tackling paramilitarism and breaking the stranglehold of terrorists and thugs on vulnerable communities."
Mr Brokenshire also attended a "working lunch" organised by the British Irish Chamber of Commerce.
He reiterated his government's commitment to "frictionless trade on the island of Ireland."
Speaking at the event Director General of the British Irish Chamber, John McGrane welcomed the commitment but warned "we are still cautious about the feasibility of these proposals and will continue to positively engage with Governments on both sides to ensure that a solution is found that works for all concerned.”