May will remain as prime minister while her successor is elected in a two-stage process under which two final candidates face a ballot of 125,000 Conservative Party members, the newspaper said.
It came after UK House of Commons Leader Andrea Leadsom, a prominent supporter of the country’s exit from the European Union (EU), stepped down over May's handling of Brexit.
Leadsom quit on Wednesday night, saying she had lost faith in the government’s approach to Brexit and therefore could not back the new Withdrawal Agreement Bill that May planned to present to the parliament on Thursday.
Speaking to reporters after her resignation, Leadsom refused to answer the question whether she wanted May to quit her job as the prime minister.
May will meet the chair of the powerful 1922 committee of Conservative lawmakers on Friday, after campaigning for the upcoming European Parliament elections on Thursday.
Her office said she was disappointed by Leadsom's decision but would nevertheless stay focused on delivering Brexit.
Message end/