THE Democratic Unionist Party has said it will not accept any Brexit deal that "separates" Northern Ireland from the rest of the UK.

DUP leader Arlene Foster said the party, which which props up Theresa May's Tory minority Government, would not allow "any form of regulatory divergence" from the UK.

She spoke out after Ireland's deputy premier Simon Coveney said the Dublin government's concerns over the post-Brexit border with Northern Ireland were set to be addressed fully, amid reports the UK would allow "regulatory alignment" between north and south.

May did not comment on the reports as she arrived for a key working lunch with Jean-Claude Juncker, which will be followed by talks with European Council president Donald Tusk.

How to maintain a soft Irish border has emerged as the key sticking point to getting agreement from the EU to move on to phase two in Brexit negotiations, but Tusk said on Monday that progress was "getting closer".

Regulatory alignment could mean both Ireland and Northern Ireland following the same rules governing trade, to ensure that goods can continue to move freely across a "soft" border with no checks.

But Foster made clear the DUP would oppose the deal if it meant the effective drawing of a new border in the Irish Sea between Northern Ireland and the rest of the UK if the Westminster Government decides it wants to diverge from EU rules.

Speaking at Stormont, she said: "We note the speculation emanating from the European Union exit talks regarding the Republic of Ireland and United Kingdom border.

"We have been very clear. Northern Ireland must leave the EU on the same terms as the rest of the United Kingdom.

"We will not accept any form of regulatory divergence which separates Northern Ireland economically or politically from the rest of the United Kingdom.

"The economic and constitutional integrity of the United Kingdom will not be compromised in any way.

"Her Majesty's Government understands the DUP position.

"The Prime Minister has told the House of Commons that there will be no border in the Irish Sea.

"The Prime Minister has been clear that the UK is leaving the European Union as a whole and the territorial and economic integrity of the United Kingdom will be protected.

"We want to see a sensible Brexit where the Common Travel Area is continued, we meet our financial obligations, have a strictly time-limited implementation period and where the contribution of EU migrants to our economy is recognised in a practical manner.

"The Republic of Ireland claim to be guarantors of the Belfast Agreement but they are clearly seeking to unilaterally change the Belfast Agreement without our input or consent."

After she finished her statement, Foster did not answer a reporter's question about the status of the confidence and supply deal.

Earlier, Irish Tanaiste Coveney said: "The indications we have is that we are in a much better place now than we have been in the negotiations to date. The legitimate concerns that Ireland has been raising for months are going to be addressed fully."

He added: "These discussions are moving in the right direction. I hope we are in a place this evening where Irish people north and south will get reassurance from the wording that is very close to being finalised now."

Coveney told RTE Radio One he believed that the post-Brexit border will be "invisible" with "no barriers" and "will look very much like it looks today".

May smiled and shook hands with Juncker as she arrived in Brussels but did not respond to reporters' questions.

Just before the lunch, Juncker and Tusk spoke to Irish Taoiseach Leo Varadkar by telephone.

Tusk tweeted: "Tell me why I like Mondays! Encouraged after my phone call with Taoiseach @campaignforleo on progress on #Brexit issue of Ireland. Getting closer to sufficient progress at December #EUCO."

The reports of a deal on regulatory alignment prompted Scottish First Minister Nicola Sturgeon to insist it would leave no reason why other parts of the UK could not effectively stay in the single market.

She tweeted: "If one part of UK can retain regulatory alignment with EU and effectively stay in the single market (which is the right solution for Northern Ireland) there is surely no good practical reason why others can't."

Lord Trimble, former leader of the Ulster Unionists and ex-Northern Ireland first minister, said he was left "shocked" and "scratching his head" at reports of a deal allowing continued regulatory alignment across the border.

He told BBC Radio 4's World At One: "We need to see the detail of this. I think it's a thoroughly bad idea. If this operates purely on a Northern Ireland basis, it's going to put Northern Ireland businesses ... potentially, at a very significant disadvantage.

"Because, they would be locked into European regulatory provisions, whereas the rest of the United Kingdom, which is their major market, is free from those, and may have different regulatory provisions entirely."

Told that he sounded shocked by reports of a deal, Lord Trimble said: "Yeah, I am, yes. Because, potentially, this is very bad news for Northern Ireland, if it happens."

Lord Trimble said he hoped that one side was giving a particular version of what was being agreed in order to try to influence events.

"I hope that there is still an opportunity for the Prime Minister to claw back from what is being said to the media at the moment."

Asked about how his colleagues in Parliament would react to such a deal, Lord Trimble, who sits as a Conservative peer, said: "I am surprised and I think my colleagues in Parliament will be surprised too.

"I am hoping that the reality is somewhat different from what is being reported.

"If it is as has been suggested, then I think this is a very, very big issue indeed."

In Westminster, Brexit Minister Steve Baker and May's chief of staff, Gavin Barwell, are expected to update Tory MPs on Brexit negotiations in Parliament at 4pm, a senior party MP told the Press Association.

London's Labour Mayor, Sadiq Khan, tweeted: "Huge ramifications for London if Theresa May has conceded that it's possible for part of the UK to remain within the single market & customs union after Brexit. Londoners overwhelmingly voted to remain in the EU and a similar deal here could protect tens of thousands of jobs."

Earlier, May's official spokesman said any agreement on the Irish border would protect the "territorial and economic integrity" of the UK.

Ahead of the meetings in Brussels, he told a regular Westminster briefing: "The PM has been clear that the UK is leaving the European Union as a whole and the territorial and economic integrity of the United Kingdom will be protected."

Responding directly to questions about the report of agreement on regulatory alignment by Irish broadcaster RTE, he said: "RTE also reported this morning we were holding a Cabinet meeting and I missed that if it occurred."

Irish Taoiseach Leo Varadkar had been due to make a statement on the developments on the steps of Government Buildings in Dublin at 2.30pm but his appearance was postponed at short notice, apparently due to the fact that talks in Brussels were continuing.