She will host Foster to thrash out the terms of the party's backing and agreement to vote with the Tories on policies in the House of Commons to get bills through.
May has said that the party, with its 10 crucial MPs to make up a majority in the House of Commons for the Conservatives, will have no veto on key policies.
The DUP is expected to make a better economic deal for Northern Ireland the central factor for any deal, officially referred to as a "confidence and supply deal".
Last evening, May faced the tough 1922 Committee of her party's backbench MPs amid a brewing rebellion within the ranks after her gamble to call a snap general election backfired, leaving the Tories eight seats short of a majority.
More From This Section
She reportedly apologised to Tory MPs, accepting personal responsibility for failing to win an outright victory and sacrificing the parliamentary majority she inherited from David Cameron when she became leader after the Brexit referendum last year.
Meanwhile, parliamentary business kicks off today as the House of Commons is set to choose a new speaker and the House of Lords will begin to be sworn in.
After chairing a Cabinet meeting followed by her meeting with the DUP leader at Downing Street, May is set to travel to Paris to hold talks with French President Emmanuel Macron. They will announce joint plans to fine social media companies such as Facebook, Twitter and Google if they fail to remove extremist content from their websites.
The two leaders will hold their bilateral dialogue as they attend a France vs England international friendly football match.
May hopes to make an ally of Macron before the formal opening of Brexit negotiations, which is expected to take place next week.
The Brexit negotiations with the European Union (EU) were set to kick off on Monday, which have now been delayed until later next week.