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Theresa May has greeted Arlene Foster on the steps of 10 Downing Street, amid speculation that a deal between the Conservatives and the DUP is imminent.
The two parties have been locked in talks for two weeks on a confidence and supply deal to prop up the Prime Minister's minority government.
Sources close to the negotiations say there are a few outstanding matters to be resolved, but these issues are not believed to be relatively minor.
An agreement would boost the Tories ahead of the crucial Queen's Speech vote on Thursday.
Despite fears a pact could complicate talks to restore the Northern Ireland Executive, Mrs Foster told Sky News she was confident her party would clinch agreements in Westminster and Stormont.
The DUP leader said: "We're back in London again and my hope is that we will be able to finalise the deal between ourselves and the Conservative Party.
"I think that this agreement will bring the prospects of doing a deal at Stormont closer because this will have a positive impact in relation to Northern Ireland.
"I very much hope that this week we will be able to conclude on two agreements."
Mrs Foster added the terms of a DUP-Conservative agreement would be "completely transparent" and made public.
The DUP is Northern Ireland's largest party, and it has made clear its 10 MPs will only support the Tories on key votes if tangible benefits are delivered in exchange - including jobs and investment in health, education and infrastructure.
Although the concession offered to the DUP is believed to be "significant", it may fall short of the £2bn which Mrs Foster's party was reportedly holding out for.
Sky News also understands that the DUP may be given some credit for the removal of less popular measures from the Queen's Speech, such as plans to abandon the triple lock on pensions and means-test winter fuel benefits.
Former Tory chairman Lord Patten has warned the Conservatives will look like the "Nasty Party" if they cut a deal with the "toxic" Democratic Unionists.
He added: "Every vote will cost you. Every vote you will have to find some way of paying for it and then explain to the Scots and the Welsh and people in the North East why they can't have the same thing too."
Some Conservatives have raised concerns about linking up with the DUP because of its opposition to same-sex marriage and abortion.
On Sunday, the DUP's leader in Westminster said those who hold different views on social issues have no reason to fear the party's influence.
Nigel Dodds told Sky News he and colleagues had been misrepresented as "dinosaurs".
He said: "People can always go back through the archives of any political party and find individuals saying things or policies from 20, 30 years ago.
"But they need to read our manifesto and look at the recent years in Northern Ireland where the DUP has been the main partner in government with republicans to move this province forward."
Source: AFP