The accolade is open to World Cup participants born on or after Jan. 1, 1993, from which FIFA's Technical Study Group will select a winner after the final.
Pogba, who won the Golden Ball prize for the best player at the 2013 Under-20 World Cup, starred in France's midfield and scored the opening goal during Les Bleus' 2-0 win over Nigeria in the round of 16.
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Varane started all but one of France's five tournament games in the center of defence and showed signs of a return to his very best Real Madrid form from the 2012-13 campaign, though he was arguably at fault for Mats Hummels' winner in the quarterfinal against Germany.
After beginning the World Cup as a substitute and entering the record books as Netherlands' youngest ever scorer against Australia, PSV star Depay cemented his place in Louis van Gaal's plans when he notched the second in the 2-0 win over Chile. Depay then became his country's youngest starter since 1938 against Costa Rica.