He said the current process - which involves the United Kingdom and Irish governments chairing elements of the negotiations and the head of the Northern Ireland Civil Service moderating other discussions - is the "right approach".
The DUP leader is nearly certain to ask for greater investment in Northern Ireland as the price of a deal.
The DUP source told BBC assistant political editor Norman Smith the two parties were now finalising the "terms and conditions" of an agreement after Mrs May and DUP leader Arlene Foster met on Tuesday.
But an alliance between May and a pro-Union party like the DUP could undermine the confidence of Northern Ireland's Catholics in the process and revive tensions in an area bordering the EU.
The Jury At Bill Cosby's Trial Can't Come To A Decision!
She added that she did not feel optimistic after hearing the jurors would continue deliberations after announcing the deadlock. Following the failure to reach a unanimous decision, the judge encouraged the 12 jury members to come to a consensus.
Now May is seeking to gain the support of the 10 DUP MPs, who have become unlikely kingmakers following last week's vote.
The Prime Minister will meet separately with representatives of Sinn Fein, the Ulster Unionists, the SDLP and the Alliance Party - as well as the DUP - in Downing Street in an attempt to allay growing concerns.
The government said it will press ahead with the State Opening of Parliament on Wednesday despite there being no guarantee of a full agreement to ensure the Conservatives can pass future legislation.
Sinn Féin Leader in the north, Michelle O'Neill, insisted that any DUP-Tory arrangement should not be allowed to undermine the peace process.
Following more than an hour of talks between May and DUP leader Arlene Foster on Tuesday, May said the discussion had been productive and Foster said she hoped a deal could be done "sooner rather than later".
Bill Cosby accuser 'froze' during alleged sex attack
She was 31 at the time and had befriended him through Temple University in Philadelphia, where he served on the board of trustees. Cosby arrived in court Wednesday along with his longtime hair stylist John Achison and Achison's wife, actress Sheila Frazier.
May made clear the Brexit negotiations would begin next despite uncertainty.
"I can't negotiate with myself", he told European newspapers including the Financial Times.
"But we do want to do so in the national interest to give stability to the government and that's why we will be entering these negotiations", she said.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.
She said: "There's been a lot of hyperbole talked about our position to the gay community".
Last day of the Bill Cosby sex assault trial
He also co-starred in the 1960s espionage show "I Spy", the first black performer to star in a weekly American TV dramatic series. He claimed that he gave Constand tablets of Benadryl, but prosecutors claimed that the comedian gave her a stronger substance.
With formal European Union divorce talks due next week, May heads to France on Tuesday to meet Emmanuel Macron, who last month swept to victory in its presidential election.
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