Clarkson was axed in March for punching producer Oisin Tymon in a row over a steak dinner.
But he told the Sun he met an unnamed BBC executive days before Chris Evans was announced as the new host.
Asked if Clarkson was offered a Top Gear return, Lord Hall told BBC1’s the Andrew Marr Show: “I have no idea what that’s all about.
“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.
“I said then that one of the things we should do is reinvent the programme, refresh the programme.”
Lord Hall also said he would like to see women in the motoring show’s presenting team and hoped the new Top Gear will appeal to old fans and those who were “put off” by parts of it in the past.
Asked again about a return offer for Clarkson, Lord Hall said: “I have no idea what that’s all about.
“What I do know is I am absolutely thrilled when I was told over a week ago that Chris had agreed to come back.”
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.”
He said he hoped the “edge” and “sense of danger” will remain with the new show, adding: “I hope it really appeals to all the people who liked the old Top Gear but we can also bring in people who maybe were put off by part of how the programme was in the past.”
Asked if he would like to see women in the presenting team, he said: “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.
“And might I say they’ve also got to think about a UK audience but also a global audience because this is a global show, a global hit and it’s important to the money we make through BBC Worldwide.”