New Education Secretary Damian Hinds was twice tipped as a future leader on Thursday by key allies of the Prime Minister.
Ms May is thought to be safe in her job at least until Brexit in 2019, but the less-than-smooth Cabinet reshuffle earlier this week has led some of her MPs to start thinking about the future again.
East Hampshire MP Mr Hinds has been talked of for months among Conservative ranks as a hope for the post-May period, but his ascent to the Cabinet has now sparked more public praise.
Mr Gove said that a future leadership contest could see Mr Hinds pitted against Defence Secretary Gavin Williamson, who has also had a meteoric rise under Ms May’s tenure at Downing Street.
Speaking to the Today programme on BBC Radio 4, he described the two as “incredibly impressive young politicians” but insisted that he wanted Ms May to lead the Tories into the next election.
Mr Timothy, who left his job following the election, wrote in The Daily Telegraph that Mr Hinds was taking on a role from Justine Greening, sacked in the reshuffle, in which he could define himself.
He said: “Greening blocked proposals to reduce tuition fees and refused to hold a proper review of tertiary education.
“Hinds must be brave enough to do just that, to ensure universities are better, fees are lower and young people get the technical or academic education that suits them.
“He is already touted as a potential prime minister: if he gets this right, he will be a convincing candidate.”
Mr Gove has previously himself stood for the Tory leadership, but failed after stabbing Boris Johnson in the back, having previously supported his candidacy.
When asked if he might stand again this morning, he said he was focused on his job as Environment Secretary.
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