Following two hours of talks at Number 10, Ms Foster said: "Discussions are going well with the Government and we hope soon to be able to bring this work to a successful conclusion".
She mocked Labour leader Jeremy Corbyn, a socialist, as incompetent and unrealistic, but his electoral campaign energised the youth vote and wiped out the Conservatives' majority in parliament.
Asked about the DUP's stance on austerity as a deal is discussed, Mr Gove said: "We don't have a majority, and one of things which I do think we need to do is to make sure that, when we bring forward a programme, it can command the broadest possible level of public confidence, and we also need to reflect on what the election result told us about the way that people want to see the economy managed in the future and I think that there is an important balance to be struck".
The DUP's social conservatism on issues such as gay marriage and abortion has been in the spotlight in Great Britain since its role as parliamentary kingmaker became clear.
DUP has won 10 seats in these elections.
May now stands accused of throwing the peace process into jeopardy by forming an alliance with the DUP at a time when London and Dublin are supposed to be neutral in finding a way to break the impasse of the forming of a Northern Ireland Executive.
Former Conservative prime minister John Major has also raised doubts about the deal and its impact on the province's "fragile" peace, telling BBC radio that the government "will not be seen to be impartial" if locked into a deal.
This would result in the United Kingdom remaining a member of the Customs Union, the European Court of Justice having a limited say over British law, and a trade deal that allows Britain access to the Single Market in exchange for accepting the free movement of people.
"This new arrangement is very unsettling and people are concerned and anxious about what it may mean", Sinn Fein MP Michelle Glidernew told AFP.
Having helped deliver a number of major events to Northern Ireland, such as the Giro d'Italia and golf's Open Championship, the DUP may ask for support hosting other high-profile global show-pieces.
Deflated Wawrinka says he was too hesitant in French Open final
Nadal now has 15 major titles, separating himself from his tie with Pete Sampras for second-most in tennis history. Wawrinka suffered his first defeat in four Slam finals and simply conceded he was no match for Nadal.
Sky's Ireland Correspondent David Blevins reports that DUP leader Arlene Foster is not returning to Belfast on Tuesday as planned, which could suggest a deal is not far away.
The demand has gained ground because the election results have created political chaos ahead of Brexit talks with the European Union set to start next week.
The European Union (EU) will keep the door open for Britain to return, but only on worse terms than it now has, EU Parliament Brexit negotiator Guy Verhofstadt said Wednesday.
In a poisonous briefing to The Guardian's Jennifer Rankin, figures in the European Union said British civil servants are keen to start formal negotiations but are being delayed by the political turmoil in Westminster.
"My preoccupation is that time is passing, it is passing quicker than anyone believes because the subjects we have to deal with are extraordinarily complex", he added.
Macron said during a press conference with May in Paris on Tuesday that "of course the door is always open as long as the negotiations on Brexit have not finished."Earlier, German Finance Minister Wolfgang Schaeuble made very similar comments on the possibility of Britain staying in the EU".
It is the latest barb by the European Parliament's chief negotiator who yesterday demanded Britain urgently clarifies its position and abandon plans for a "hard Brexit".
A DUP source said: "Our discussions are continuing".
But Ruth Davidson, the pro-EU leader of the Conservatives in Scotland, called on May to "reopen" the government's Brexit plans.
The draft law would empower Europe to decide if post-Brexit London has the right to host financial market "clearing houses" that deal in euros, the EU's single currency.
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