Farah, 33, secured a historic 'double double' by retaining both his 5,000m and 10,000m Olympic titles at Rio 2016.
Paula Radcliffe, in 2002, was the last British athlete to win one of the IAAF's end-of-year awards.
Farah faces competition from the likes of Jamaican sprinter Usain Bolt - a nine-time Olympic gold medallist - and South Africa's Wayde van Niekerk.
He broke Michael Johnson's 17-year-old 400m world record to claim victory in Rio.
The winner of both the male and female awards will be announced at the IAAF awards dinner in Monaco in December.
The last Briton to win the men's award was triple jumper Jonathan Edwards in 1995, the year in which he jumped 18.29m, which is still the world record.
South Africa's Olympic 800m champion Caster Semenya is among those nominated for female athlete of the year.
The 25-year-old won gold in Rio to add to her silver medal from London 2012.
Her rivals include Ethiopia's Almaz Ayana, who broke the 10,000m world record by over 14 seconds in Rio, and Spain's Ruth Beitia, who won Olympic high jump gold aged 37.