MPs are looking at whether the foreign affairs watchdog or ethics officials in the Cabinet Office could investigate Boris Johnson’s proposal to give a senior job to his then girlfriend in 2018, after the prime minister refused to deny having done so. Johnson fuelled speculation that he attempted to install Carrie Johnson, now his wife, as his chief of staff when foreign secretary after he declined to comment on the allegations at prime minister’s questions. Asked about reports that he tried to get her appointed to a Foreign Office job, and two other roles including one with a royal charity, Johnson simply ignored the subject. The Labour MP Chris Elmore asked Johnson: “Has he ever considered the appointment of his current spouse to a government post or to any organisation in the working of the royal households? Be honest, prime minister, yes or no?” Johnson replied: “I know why the party opposite wants to talk about nonexistent jobs, in the media. Because they don’t want to talk about what is going on in the real world.” He then went on to discuss employment statistics. Keir Starmer openly mocked Johnson over the issue later in PMQs. After Johnson noted that Labour MPs had visited rail strike picket lines, the Labour leader replied: “I’m surprised he’s giving me advice about my team. If I do need advice – let’s say about a £100,000 a year job at the Foreign Office – I will ask him for a recommendation.” MPs, including some Conservatives, are considering how to prompt an investigation into the allegations given there is currently no adviser on ministerial propriety after Lord Geidt resigned from the role. Some members of the foreign affairs committee are contemplating an inquiry into the allegations. Another option is calling for the Cabinet Office’s ethics officials to investigate, given it relates to a civil service appointment. It is believed to be difficult for the standards committee to look into the allegations without a prior investigation by the standards commissioner, whose remit covers the work of MPs rather than ministerial roles. Downing Street continues to claim there is nothing to investigate and that the story is untrue, after admitting that No 10 did intervene to get the story pulled from the Times over the weekend. Earlier, the deputy prime minister, Dominic Raab, said Carrie Johnson was being targeted in a “deeply unsavoury” political attack. Speaking to Sky News, he batted away calls for an investigation into the allegations, which Labour’s Chris Bryant, the standards committee chair, said appeared to be a case of corruption. The claims were first made in a book by the Tory peer Lord Ashcroft and came into the spotlight again after the Times withdrew an article going into more detail about how Johnson had tried to get his now wife a £100,000 post at the Foreign Office when he was foreign secretary in 2018. Johnson was still married to Marina Wheeler at the time. No 10 later admitted having intervened to stop the article from running, despite the journalist who wrote the story, Simon Walters, standing by it. The Guardian has also been told by sources that the story is true, with one saying evidence exists that Johnson tried to get his then girlfriend a job. Asked whether there should be an investigation, Raab said: “These attacks on Carrie are deeply unsavoury. The allegations have been roundly responded to as flawed. Those are matters for No 10 and Carrie. But frankly, what I think you’re seeing is a political attack on Carrie as a way of getting to the prime minister and that’s out of order.” He added that there was a “feeding frenzy on anything thrown out there as a claim against the prime minister and his wife and I think that’s wrong”. The prime minister’s spokesperson has previously said they were unable to comment on Johnson’s activities before he became prime minister, but that “others have made clear this story is untrue”. The former Foreign Office minister Alan Duncan said he was told in 2018 that Carrie Johnson was a rising star running communications in Conservative campaign headquarters (CCHQ) and was being lined up for a special adviser role in the department. “For someone slightly unproven who knew nothing about foreign affairs to come straight out of CCHQ and into the Foreign Office was rather noticeable,” Duncan told the Guardian. On Tuesday, Bryant called for the “paper trail” surrounding the issue to be published. “It is manifestly corrupt to appoint your lover as a spad,” he said in a tweet. Carrie Johnson’s spokesperson has called the claims about her being offered a job in the Foreign Office “totally untrue”. On the subsequent claims about attempts to find her a job elsewhere, they said: “This is an old story, as untrue now as it was then.”