The DUP source, speaking on condition of anonymity, said it was possible that a deal was possible this week as it was agreed in principle, but some details needed to be tied down.
Last week, Sinn Fein's Gerry Adams went to Downing Street and told Theresa May that an agreement with the DUP would constitute a breach of the Good Friday Agreement, making clear his party will continue to demand a "unity poll", referred to by the Good Friday Agreement as a "border poll".
"I am very reassured by what the prime minister said to me today that that won't be the case".
SP Supremo Mulayam Singh Yadav Backs NDA Presidential Nominee Ram Nath Kovind
It should be noted that Bihar Governor Ram Nath Kovind has been decided as NDA's presidential candidate. Kovind as the Governor of Bihar, a communiqué issued by the Rashtrapati Bhavan said on June 20, 2017.
Speaking after his first meeting with European Union chief Brexit negotiator Michel Barnier since being appointed to his new role, Mr Coveney said Ireland's unique circumstances are well understood in Brussels.
However, the focus on Monday was on the viability of the Good Friday Agreement. He said there were enormous technical difficulties with trade issues which could mean this question might not be resolved until the end of the talks process.
The talks are taking place as the DUP and Tories attempt to strike a separate deal to prop up British Prime Minister Theresa May's minority government. The Agreement also makes Dublin a co-guarantor of the agreement.
'Weapons stash found at Champs-Elysees attacker's home'
The weapons and explosives found in the vehicle "could potentially blow this auto up", he added. The driver's vehicle (seen in the picture below) then exploded into flames.
The Good Friday Agreement gives the United Kingdom government - now dependent on the DUP vote of confidence - the role of "a broker" between the two communities.
"I am personally committed to ensuring a practical solution that recognises the unique economic, social, cultural and political context of the land Border with Ireland - which so many people pass through every day and it remain our priority to work closely with the Irish Government to ensure a frictionless and seamless a border as possible", she said.
Northern Ireland has been without a government since March after the DUP and Sinn Fein could not reach a power-sharing agreement following Assembly elections, with the latter refusing to enter Stormont with Arlene Foster as first minister.
UPS gunman had overtime grievance against firm - union
They told her to run because there had been a shooting, she told CNN, explaining she ran about a block with the workers. Wednesday's shooting prompted a massive police response in a neighbourhood near the California city's downtown area.
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