Johnson said this in a conversation with a member of the House of Lords and Lord Craddas.
“He said he would like to remain prime minister.
He said he didn't want to resign," Kraddas was quoted as saying by the newspaper.
On July 7, Johnson announced his decision to step down as Prime Minister of Great Britain and leader of the country's Conservative Party.
He will continue to fulfill his duties until the election of a new head of the cabinet of ministers.
Former Chancellor of the Treasury Rishi Sunak, Undersecretary of Commerce Penny Mordaunt and Foreign Secretary Liz Truss are participating in the elections for the post of British Prime Minister.