Sir Chris Hoy and Andy Murray have also been nominated after a great year that saw the 36-year-old cyclist become Britain's most successful Olympian with six gold medals in total.
Tennis star Murray, 27, won the US Open, his first major grand slam tournament.
He also won gold in the Olympics men's singles along with silver in the mixed doubles.
Rower Grainger, 37, delighted the crowd and millions of TV viewers when she took gold in the double sculls with Anna Watkins at the London Olympics.
Olympic and Paralympic champions dominate the shortlist for the BBC Sports Personality of the Year award.
Top cyclist Bradley Wiggins, athletes Mo Farah and David Weir, sailor Ben Ainslie are in the mix for the coveted award.
Heptathlete Jessica Ennis, cyclist Sarah Storey, boxer Nicola Adams, swimmer Ellie Simmonds and golfer Rory McIlroy are also in the running.
Last year, not a single woman made it on to the final shortlist, despite a strong year of competition.
The controversy has triggered a review of the process for this year's event, which has also produced a shortlist that includes two more sports personalities than usual.
An expert panel has also been introduced.
After a golden summer of home-grown sport, including the London 2012 Games, the event promises to be the biggest in the programme's 59-year history.
The winner will be announced at the televised ceremony in London on December 16.