Media mogul Rupert Murdoch attended a joint media interview with US President Donald Trump last month, despite photographs and video of the event showing only Trump and the two interviewers, the Financial Times reports.

The Times and German tabloid Bild published photographs and video of the interview with Trump - conducted just days before Trump's inauguration - at his office in Trump Tower in New York, showing only those three people.

But the FT said two sources had told it that Australia's Murdoch, 85, whose News Corp owns The Times, was "sitting in on the conversation".

It said Murdoch's presence reflected his "interest in Mr Trump and his close relationship with the new president and his family".

Conservative lawmaker Michael Gove, a former journalist who lost out to UK Prime Minister Theresa May in a party leadership election in July, asked questions for The Times.

Contacted by telephone, News UK - the News Corp subsidiary running The Times and The Sun in Britain - declined to comment on Murdoch's reported attendance at the Trump interview.

Murdoch - who also runs US broadcaster Fox News - and his family have several links to the Trump and Gove families.

Days before Gove announced his leadership bid, Murdoch told a business summit in London that Gove was "the most principled and most able" candidate.

The FT reported earlier that Trump's daughter, Ivanka, acted as a trustee for shares owned by Murdoch's two youngest daughters in 21st Century Fox and News Corp.

Murdoch also developed close ties to former British prime ministers David Cameron and Tony Blair.