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Hull sacked manager Mike Phelan on Tuesday night, a day after the Tigers lost 3-1 at West Bromwich Albion despite taking the lead at the Hawthorns.
Sherwood is not a leading candidate for the Premier League strugglers, who are three points adrift of safety in England's top flight, with Gary Rowett the favourite for the vacancy.
After recently-sacked Birmingham boss Rowett, Marco Silva (previously of Olympiakos), Alan Pardew and Jaap Stam (Reading) follow and then Sherwood who has odds of 18/1 on Bet365.
William Hill price Sherwood at 25/1, as do SkyBet.
Sherwood is not contracted at Swindon which means Hull would not have to pay compensation for the ex-Tottenham and Aston Villa manager who led the latter to the FA Cup final and Premier League survival in 2015.
When sacked by Villa Sherwood was due a compensation fee that would only be waivered if he accepted another job before October 2016. He joined Swindon in November so got his entire fee due from the Villians, who got relegated after sacking Sherwood.
He is also priced at 20/1 for the England Under-21 post with Oxford's Michael Appleton the favourite for that followed by Mark Warburton (Rangers), Neal Ardley (AFC Wimbledon), Steve Cotterill and Paul Ince.
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