The Hollywood star of movies like Wanted and Salt has never appeared on the BBC Two motoring show, and Richard - who presents the programme alongside Jeremy Clarkson and James May - reckons she might be a good competitor in the Star In A Reasonably Priced Car challenge.
"I'd like to see Angelina Jolie just because she's lovely - I'd be really embarrassed, I'd be terrible, I'd just be hiding all the time," he said.
"I'd be sick with nerves because she's really beautiful and I'd be scared."
Richard, who is hosting the Carphone Warehouse Appys in London on April 11, revealed he doesn't have much say with the celebrities that come on the show."I'm not massively involved in that part of the show, to be brutally honest. It helped when Jonathan Ross came off air because all the big celebs came to us, hence Tom Cruise and Cameron Diaz suddenly turned up," he added.
His favourite guest is acclaimed actor Michael Gambon, who has appeared twice.
"It's always lovely seeing Michael Gambon. Top bloke, genuine enthusiasm," he recalled.
"He pitches up at the track before everyone else, standing around and looking at the cars, I think he's a real enthusiast. Really good company and a great actor."
