The 54-year-old has featured on the popular show a dozen times since Angus Deayton left in 2002. He famously threw a pen at team captain Ian Hislop during a 2008 episode, leaving him with a cut on his face.
"We had to stop recording," said Hislop. "He refused to believe it was blood. He said it was red biro and then apologised to me afterwards."
Jimmy Mulville from production company Hat Trick, which makes Have I Got News For You, told the Broadcasting Press Guild last month that he thought Clarkson was "a fantastic broadcaster", adding that they should "get the producer on so he can hit Jeremy Clarkson live on television".
Clarkson's wider future remains unclear, although North Yorkshire Police announced yesterday that he will not face police action over his attack on Tymon, which happened at a hotel in the area.
It emerged last week that he will still appear on stage with former Top Gear colleagues Richard Hammond and James May to fulfil a series of live shows planned before he left the BBC.
The events will be stripped of all BBC branding and content and billed as Clarkson, Hammond and May Live.
That means the shows, which will take in venues in Australia, Norway, South Africa and the UK, will not be able to use clips from Top Gear or feature The Stig.
The move has sparked rumours that the three men intend to team up to continue their careers together after Clarkson's exit from the corporation, but sources close to the tour say it is simply a matter of not wanting to disappoint fans.
The future of the show's other two presenters, Hammond and May, is also in doubt, with both men's Top Gear contracts having run out.
Police are still investigating threats to kill Hall, reportedly linked to his decision to axe Clarkson. The former chief executive of the Royal Opera House took over the £450,000 BBC post in April 2013 to replace George Entwistle, who left the corporation in the wake of the Jimmy Savile sex abuse scandal.
* The finale of Top Gear's latest season screens on TV3 at 7.30pm tonight.
- Independent