Ethiopian distance runner Almaz Ayana made the shortlist in recognition of her stunning 10,000 metres victory in Rio.
Bolt, a five-time former winner of the award, became the first person to win three consecutive 100 and 200 metres Olympic golds in Rio de Janeiro in August.
He also holds the world records in the two disciplines, 9.58 seconds and 19.19 seconds, respectively.
Thompson matched Bolt's feat by also winning the 100m and 200m golds in Rio.
