Or she could seek to govern through a so-called "confidence and supply" arrangement with other parties, in which they agree to support the minority government on vital matters, such as the Queen's Speech or the budget, in return for concessions.
May responded that the DUP deal "would provide stability and certainty for the United Kingdom going forward", her office said.
In a short statement outside Downing Street after an audience with the Queen, May said she would join with her DUP "friends" to "get to work" on Brexit.
The DUP has proved hugely controversial in the past over the homophobic and sectarian views of some of its representatives.
Mrs May faced calls from within her own party to consider her own position after the election, which she brought forward by three years in the hope it would deliver her a comfortable Commons majority, ended with Labour making significant advances.
Sunday's newspapers were unsparing, with The Observer writing: "Discredited, humiliated, diminished".
The Mail on Sunday reported that Foreign Secretary Boris Johnson was set to launch a bid to oust May, while the Sunday Times said five cabinet ministers were urging him to do so.
With Home Secretary Amber Rudd, Brexit Secretary David Davis, and Defence Secretary Sir Michael Fallon all retaining their posts, there was speculation any reshuffle could be limited to replacing the eight ministers who lost their seats in the election. "She made the election a referendum on Theresa May and she has lost".
Shoot commences for Prabhas' Saaho
Some sources say that earlier for this lead female character role the filmmakers approached Shraddha Kapoor and Katrina Kapoor. Featuring a clean-shaven look for the film, the Baahubali actor was the hot topic on the internet for the past few days.
But media reports suggest they had demanded the departure of May's joint chiefs of staff, Nick Timothy and Fiona Hill, as the price for allowing the 60-year-old vicar's daughter to stay in office.
"The priority must be for politicians to get their house in order and form a functioning government, reassure the markets and protect our resilient economy".
After confirming on Friday that her top five ministers, including finance minister Philip Hammond, would keep their jobs, May must name the rest of her team, who will take on one of the most demanding jobs in recent British history.
Many critics, including Scottish Conservative leader Ruth Davidson, have expressed concerns over the DUP's stances against gay marriage and abortion, among other issues. "I would have thought that is enough for her to go, actually".
A source close to Davidson, who is gay, told the BBC: "The PM needs to remember there are more Scottish Conservatives than DUP MPs". While the DUP has always been Eurosceptic, it does not want to see a hard border between Northern Ireland and the Republic.
The DUP's stated goal is as the unionist party, meaning they do not support the idea of Northern Irish independence from the UK.
With Britain due to start negotiating the terms of its exit from the European Union with the bloc's 27 other members on June 19, the political crisis in London could not have come at a worse time.
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