Jeremy Hunt, the foreign secretary, and Sajid Javid, the home secretary, have also been mentioned as candidate, the Times reported.
Update 5:55 a.m. EDT May 24: Theresa May became prime minister of Britain after a June 2016 referendum, when the country voted to leave the European Union, The Washington Post reported.
May tried three times to get Parliament to pass the Brexit withdrawal but the House of Commons rejected it each time, the newspaper reported.
That led to her resignation Friday.
"I will shortly leave the job that it has been the honor of my life to hold,” May said outside 10 Downing Street. “The second female prime minister, but certainly not the last."I do so with no ill will, but with enormous and enduring gratitude to have had the opportunity to serve the country I love."
Boris Johnson, who once said his chances of becoming prime minister were "about as good as the chances of finding Elvis on Mars," is now the favorite to become Britain's 77th prime minister, according to the Post.
Update 5:35 a.m. EDT May 24: Prime Minister Theresa May's voice shook with emotion as she announced her resignation Friday morning, saying she had "done my best" to try to get Britain out of the European Union, the BBC reported.
May said she would step down as leader of the Conservative party on June 7, but will remain prime minister until a successor is chosen, The New York Times reported.
“I believe I was right to persevere, even when the odds against success seemed high,” May said. “But it is now clear to me that it is in the best interests of the country for a new prime minister to lead that effort.”
May will still be in office when President Donald Trump arrives in Britain on June 3 for a state visit, which will coincide with events marking the 75th anniversary of the D-Day landings during World War II.
May had been under pressure to resign after a backlash by her own party against her latest Brexit plan, the BBC reported.