Theresa May is expected to take a decision on Damian Green’s future this week as the cabinet inquiry into his conduct concludes.
The prime minister will have to make a judgment about two issues of fact on which the investigation hinges, The Times understands.
Mr Green, 61, who as first secretary of state is Mrs May’s deputy, was placed under investigation last month by Sue Gray, the Cabinet Office director-general for propriety and ethics, after Kate Maltby, a Tory activist, accused him of making inappropriate advances towards her. He denies the allegation.
Two retired Scotland Yard detectives then claimed that during a police raid on his Westminster office in 2008, pornographic images were discovered on a computer, which he also denies.