The cyclist, who won two gold medals in the velodrome at London 2012, said he would be happy for either the Tour de France champion or tennis ace to win after "an exceptional year" for British sport.
Speaking to Digital Spy, Hoy said: "I feel bad saying this because there's so many people that will go, 'What about this person? What about this person?' [but] I'd have to vote for Bradley Wiggins.
"To win the Tour de France, [be the] first ever British rider not just to win, but to get on the podium, coupled with the fact he's Olympic champion, [has] won now seven medals at Olympic Games over the years. [He's] fantastic for the sport, fantastic for Britain.
"At the same time you think Andy Murray - US open, Olympic gold medal, finalist in Wimbledon, Olympic silver medal. So, one of those two."
He continued: "Any one of the last ten in a normal year, you'd happily say, 'Yeah, they're a deserving winner'. It's just that this year is an exceptional year."
Despite becoming the most successful British Olympian of all time at the Games, and the joint most decorated with Wiggins, Hoy wasn't confident about his own chances, arguing that there are "better" athletes with a "more worth reason for winning" on the shortlist.
"If I could make the last ten, I'd be delighted to be part of it and be part of a historic year, but I'm certainly not expecting to win it or place in the top three," he said.
Wiggins has also been backed to win BBC Sports Personality of the Year by Digital Spy readers, collecting 23.4% of the vote in our exclusive poll.
Other Olympic and Paralympic athletes nominated for the prize are Jessica Ennis, Mo Farah, Ellie Simmonds, Katherine Grainger, Ben Ainslie, Nicola Adams, Sarah Storey and David Weir.
Golfer Rory McIlroy is the only candidate not to have competed at London 2012.
Sports Personality, which is being hosted by Sue Barker, Gary Lineker and Clare Balding, takes place at the ExCel Centre in London on Sunday, December 16 at 7.30pm and will air live on BBC One.