The Conservatives lost their House of Commons majority in Thursday's election and will not be able to govern without support from the DUP's 10 members of parliament.
"We had very good discussions yesterday with the Conservative Party in relation to how we could support them in forming a national government, one that would bring stability to the nation and those discussions continue. We have made good progress but the discussions continue," DUP leader Arlene Foster told Sky News.
The TV channel said Foster had told them she would be travelling to London to meet May at her official Downing Street residence on Tuesday.
(Reporting by Estelle Shirbon, Editing by Kylie MacLellan)