Wright was eliminated at Pipeline by Brazilian Dora in the round of 32 but has scored enough points to be one of 18 male surfers on the World Surf League tour to provisionally qualify for the Olympics.
Wilson is 11th in the rankings and progression to the quarter-finals would make it impossible for Freestone to overtake him.
Freestone faces Kiwi Ricardo Christie in the last 16 and needs to win the event at Pipeline and hope for Wilson to lose to Dora if he is to grab one of Australia’s spots in Tokyo.
Bailey will face two-times world champion John John Florence needing to claim a maiden WSL title to retain his championship tour status.
Meanwhile, Italo Ferreira and Gabriel Medina of Brazil and American Kolohe Andino – who have all qualified for the Olympics – remain in contention for the world title with the trio in the round of 16.