She said: "Discussions are going well with the Government and we hope soon to be able to bring this work to a successful conclusion".
Last night, Downing Street sources would only say talks were "going well".
'I think there is a unity of objective among people in the United Kingdom, ' May said following a meeting with French President Emmanuel Macron on Tuesday.
On Tuesday afternoon, Foster indicated that a deal was close to being finalised.
Sir John said he was "concerned" about the DUP deal, and said he is "wary" and "dubious" about the deal "both for peace process reasons but also for others reasons as well". She will nearly certainly ask for greater investment in Northern Ireland as part of the deal, as well as guarantees on support for pension plans and for winter fuel allowances for older people.
Mrs May's largely unchanged Cabinet earlier discussed plans for the scope of negotiations in a meeting that lasted around 90 minutes.
The senior Conservative source said dialogue with the DUP was "constant" and that the Northern Irish party supported the principles of the governing party on strengthening the union between Scotland, England, Wales and Northern Ireland, combatting terrorism and delivering Brexit.
Her failure to win a majority has put May under pressure over her Brexit plans from inside and outside her party and has prompted complaints about her choice of partner due to the DUP's stance on social issues such as gay marriage.
Trump acknowledges Russia probe includes him
Nor did he deny he has entered the miniscule ranks of sitting presidents who have become the subject of a criminal investigation. Mueller is now leading the investigation into whether Russian Federation interfered in the 2016 presidential election.
Days after Mrs May lost her parliamentary majority in a failed electoral gamble, she welcomed the leader of the DUP to Downing Street in a bid to gain the support of its 10 MPs.
May said on Tuesday that talks with the DUP had been productive - a view shared by DUP leader Arlene Foster - and that Brexit negotiations would begin as planned next week. "There's a lot of anxiety", Sinn Fein MP Michelle Gildernew told AFP.
They have previously blocked same-sex marriage being legalised in Northern Ireland.
"The DUP may never have the political arithmetic so favourable again so like the Conservatives, the DUP will want to avoid another election and will want to keep drinking in the political free bar that is available to it", Tonge said.
"But it's also really important we make sure the Brexit deal we secure is one that's in the interests of the whole country and that means that we need to ensure that those who voted Remain are part of the conversation about what the best deal for Britain is in the future".
The PM told the backbench 1922 Committee on Monday a deal with the DUP would not affect power-sharing talks in Northern Ireland or LGBT rights.
Mrs May's rivals have also warned the government's claimed impartiality as a mediator in the Northern Ireland political dispute would be fatally undermined by the DUP pact.
Sinn Fein, the SDLP and Alliance have all made clear Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore power sharing at Stormont due to their perception he has a conflict of interest.
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