Conservatives and the DUP are committed to strengthening British unity, delivering Brexit, combating terrorism, and delivering prosperity but "at the moment there isn't a deal", the source said.
And she urged the political parties here to reach agreement at home so that the Northern Ireland Assembly could get back up and running.
The Queen's Speech was today delayed while talks between the two parties take place.
The Conservatives need the DUP's 10 votes to achieve a working majority in parliament but some politicians and commentators have expressed fears that it could undermine the peace settlement that brought an end to three decades of violence in Northern Ireland.
The DUP said the talks "so far have been positive" and that "discussions will continue next week to work on the details and to reach agreement on arrangements for the new parliament".
If the parties can not agree a deal, then devolution will be suspended and the Northern Irish assembly's powers returned to the United Kingdom government.
Sinn Fein, the SDLP and Alliance have all made clear Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore powersharing at Stormont due to their perception he has a conflict of interest.
Before travelling to the French capital, Mrs May had been leading the talks with the DUP.
Merkel: EU is 'ready to start Brexit negotiations'
The election led to a hung parliament after the Tories won 318 seats, down from 330 they got in 2015. We know when they must end. "Do your best to avoid a "no deal" as result of "no negotiations".
The Prime Minister held talks with Mrs Foster in Downing Street earlier this week as she seeks to make the best of the election debacle.
The leadership of Sinn Féin will meet with British Prime Minister Theresa May in Downing Street on Thursday to discuss the potential ramifications of a deal between the Tories and the Democratic Unionist Party on a return to power-sharing in Northern Ireland.
Lord Hain, who was Northern Ireland secretary from 2005 to 2007, warned that the situation is "very damaging" at a time when sensitive talks are under way over the restoration of powersharing at Stormont.
Brexit Secretary David Davis has admitted that parts of his party's manifesto have had to be "pruned away" because they could not command support from the Commons.
May is due to meet the leaders of all five Northern Ireland political parties, June 15, in an effort to try and form a consensus over power-sharing, following the fallout between Sinn Fein and the DUP in January, when Sinn Fein's Martin McGuinness resigned as deputy First Minister, throwing the executive - the devolved government - into chaos.
Michelle O'Neill, Sinn Fein's leader in Northern Ireland, said any deal between the Conservatives and the DUP "cannot be allowed to undermine" the province's peace accords.
But he added that Sinn Fein would support any additional money going to the Northern Ireland Executive as a result of a deal.
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