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.
Ayana broke a 23-year-old record to win the 10,000 metres after clocking 29:18.45 at the Rio Games where she also took the bronze in 5,000 metres.
Bolt was joined on the men's list by two-time 5,000 and 10,000 metres Olympic champion Mo Farah of Britain and South African Wayde van Niekerk, the double 400m Olympic champion.
Anita Wlodarczyk of Poland also made the women's list after retaining her hammer title in Rio.
The finalists were determined by the IAAF Council, the IAAF Family and the public vote via social media.
The winners will be announced in Monaco next month.
(Reporting by Debanjan Bose in Bengaluru; editing by Martyn Herman)
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