Holly, who used to be BBC Radio 5 Live’s F1 pit-lane reporter, is thought to be the current frontrunner to join the show when it is relaunched next year.
Chris and Holly go way back, having previously dated as well as working together at Virgin Radio, Radio 1 and on Channel 4’s ‘TFI Friday’.
Chris recently revealed that he was ‘champing at the bit’ to get started on the show, which is expected to launch in Spring next year.
“We are ready to roll. We are now champing at the bit and getting far too hysterical for our own good,” he told ‘Top Gear’ magazine.
A BBC spokeswoman said of Holly: “We are not commenting on speculation.”
Possible 'Top Gear' Presenters
Guy Martin (01 of14)
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Guy Martin is another star whose name has been mentioned often in relation to the presenting roles.
Jodie Kidd (02 of14)
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Jodie was spotted enjoying lunch with Jeremy Clarkson in the wake of his sacking - does she already have his blessing? (credit:Richard Shotwell/Invision/AP)
Suzi's name has also come up often, during talk of a shortlist. (credit:Dave J Hogan via Getty Images)
Philip Glenister (05 of14)
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The actor's name has popped up often, and in May it was reported that he was in "advanced talks" with the BBC. (credit:Jon furniss/Invision/AP)
Will Mellor(06 of14)
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In April, sources revealed that bosses were considering Will, in the hope that he'd bring "a younger audience" to the show. (credit:David M. Benett via Getty Images)
David Hasselhoff (07 of14)
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The Hoff threw his hat into the ring last month, answering with a simple, "Why not?", when asked whether he'd be up for presenting the motoring show. (credit:KGC-143/STAR MAX/IPx)
Stephen Fry(08 of14)
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Bookies William Hill are offering odds of 10/1 on TV star Stephen nabbing the role. (credit:ASSOCIATED PRESS)
James Blunt(09 of14)
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James Blunt's also made the bookies' shortlist with odds of 12/1. (credit:ASSOCIATED PRESS)
Dermot O'Leary(10 of14)
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Dermot's left the 'X Factor' behind, and he's already on the Beeb's books thanks to his Radio 2 show. (credit:Stuart C. Wilson via Getty Images)
Jake Humphrey(11 of14)
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BT vision presenter Jake Humphrey is 8/1 to be a co-host. (credit:Karwai Tang via Getty Images)
Jamiroquai (12 of14)
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Jamiroquai loves his cars - could he make the move to television? (credit:Sowetan via Getty Images)
Adrian Chiles (13 of14)
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Well... he's not doing much at the moment is he? (credit:Tristan Fewings via Getty Images)
Nigel Mansell(14 of14)
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We reckon former Formula One World Champion Nigel Mansell would be a perfect choice. (credit:ASSOCIATED PRESS)