The Scot won his first Grand Slam at the US Open, a historic Olympic gold at Wimbledon and reached the men's singles final at SW19.
He is joined in the 12-strong shortlist by two fellow Scots – cyclist Sir Chris Hoy and Olympic gold medal-winning rower Katherine Grainger.
Murray, 27 is the third favourite to scoop the accolade at the ceremony in London next month at odds of 8/1.
The Dunblane-born player is ranked only behind Tour de France champion Bradley Wiggins with odds of 2/5 and Olympic gold medal-winning distance runner Mo Farah, who is ranked 5/1 to win.
Murray ended the tennis season ranked number three in the world after a year which saw him break down in tears after losing his first Wimbledon final to Roger Federer, only to defeat the Swiss star a month later in the Olympic final.
Weeks after his gold medal victory, Murray was hailed as a national hero when he became the first British male singles player to win a Grand Slam in 76 years when he saw off world number one Novak Djokovic at the US Open in New York.
Sir Chris, 36, became Britain's greatest ever Olympian when he surpassed Sir Steve Redgrave's previous record of five gold medals. The Edinburgh-born cyclist has now won six.
He was named BBC Sports Personality of the year in 2008 but is only ranked 50/1 to take the crown again next month.
Gold medal-winning rower Grainger cements a successful year for Scots sports personalities.
Glasgow-born Grainger, 37, topped the podium for the first time at the London Games after winning the double sculls. She is ranked 250/1 to take the title.
Her team-mates in the women's squad reacted with delight at her nomination.
In a statement, they said: "She's the kind of athlete who is there, day in and day out, setting a benchmark for the team and training alongside such an outstanding individual has without a doubt raised the standard of the GB Women's squad to what it is today."
The winner will be decided by a public vote on the night of the ceremony on December 16, with 15,000 people due at London's ExCel Arena.
Unlike last year, this ceremony features both sexes.
Alongside Grainger, heptathlete Jessica Ennis, cyclist Sarah Storey, boxer Nicola Adams, and swimmer Ellie Simmonds are also contenders.
Among the other nominees is Northern Irish golfer Rory McIlroy, 23, who established himself this year as world number one, topping the prizewinning list in Europe and the US.
He was also a key member of the European Ryder Cup team which beat the US.
Yachtman Ben Ainslie, 35, a four-time Olympic champion, is also in the running.