Among the six African athletes nominated for the esteemed award is the South African 400m world record holder Wayde van Niekerk, Kenya's female 5,000m marathon champion Hellen Obiri, and Ethiopia's long-distance female runner Almaz Ayana Eba.
The only sprinter to capture the 100 and 200-metre track titles at three consecutive Olympics, Bolt retired after this year's World Championships in London.
Barshim, a world champion and Olympic medalist, is one of the 10 men nominated for the prestigious prize by the world body.
Olympic gold medallist and three-time champion over 800m Caster Semenya will also challenge Obiri in her quest to become the first Kenyan female victor of the award.
The 35-year-old Gatlin beat Bolt into third to win gold in London in August.
Kenya's 5,000m victor Hellen Obiri, Australia's 100m hurdles gold medallist Sally Pearson and South African 800m champion Caster Semenya are the other track nominees on the shortlist.
Another notable nominee is Australia's Sally Pearson, who claimed gold in the women's 100m hurdles in 12.60 seconds.
The finalists will be determined through a three-way voting process involving the IAAF Council, the IAAF Family, and track and field fans.
Votes from the IAAF Council will count for 50 per cent of the result with the family and fan ballots counting for 25 per cent each.
Voting closes on October 16 and the winners will be announced at the awards ceremony in Monaco on November 24.
Three finalists in each category will now be decided following a voting process.
The shortlist released on Monday includes 10 men and 10 women nominees who were selected by an worldwide panel of athletics experts, comprising representatives from all six continental areas of the IAAF.