The African pair's goals were among a shortlist of 10 picked by the world football governing body, Fifa on Monday.
Oshoala, who has won the African Women's Player of the Year thrice, will crave the Goal of the Tournament accolade as a consolation for her side's Round of 16 exit.
The Barcelona star's goal sealed Nigeria's 2-0 group stage win over South Korea. The 24-year-old raced half the length of the field, dribbled past a defender, rounded the keeper and scored from a tight angle.
For Nchout, her nominated goal was one of two superb goals scored in the tournament. The chosen goal was her injury-time winner to give Cameroon a 2-1 victory over New Zealand to reach the Last 16.
The winner of the prize is currently being decided by votes on the Fifa website, which opened on Monday.