The director general of the BBC, Tony Hall, has said he would like to see women join the presenting team on Top Gear when it relaunches following the sacking of former host Jeremy Clarkson.

Clarkson was axed from the motoring programme in March after a fracas with a producer. It was announced on Tuesday that he will be replaced by Chris Evans, who will also produce the revamped Top Gear.

Lord Hall told BBC1’s Andrew Marr show: “I’d like to see some women in the presenting team but look, I also need to leave it to Chris, the team, to make up their mind about what they think is going to work best.”

Hall denied Clarkson’s claims that he had been offered his Top Gear job back. “I have no idea what that’s all about,” Hall said. “Sadly – and I say sadly because I think Jeremy Clarkson is an extraordinary talent – I announced we were parting company some months ago. I am thrilled Chris Evans has got the job.”

Questioned if it would have been appropriate for Clarkson to have received his job back, Lord Hall said: “That’s all speculation. Look, I made it absolutely clear when I said, ‘We’re going to part company’, that that was it.”

Clarkson told the Sun on Friday he had met with a BBC executive a week earlier who offered him his job back. At the time the corporation was already negotiating with Evans to take up the role.

Clarkson said he refused the request and claimed he was in talks for a new motoring programme on another station with his former Top Gear co-presenters, James May and Richard Hammond. Evans, who had previously insisted he didn’t want Clarkson’s old job, hit back on his Radio 2 breakfast show, saying Clarkson had said no to voices “in his own head”.

But now Carol Vorderman, the former Countdown presenter, has told the Sun on Sunday she witnessed the meeting between Clarkson and the BBC executive at the May Fair hotel in London. “Jeremy came over immediately and we had a chat and he told me what happened,” Vorderman said. “I am assuming he was telling the truth. We chatted for a few minutes.”

ITV, Netflix and Amazon are understood to be the frontrunners to sign Clarkson. All three companies would look to exploit the presenters’ global appeal. During his time with the show, Top Gear expanded its fan base to 350 million viewers worldwide.