If either Contepomi or Hernandez were successful it would be the first time a player from Argentina, who have reached their first-ever World Cup semi-final, won the coveted title.
France centre Yannick Jauzion, South Africa wing Bryan Habana and New Zealand captain Richie McCaw, who won the award last year, have also been shortlisted.
It is particularly significant that two Pumas should be shortlisted as Argentina do not take part in an annual international competition. Flyhalf Hernandez, who also helped Stade Francais win the French club championship this year, has been at the helm of Argentina's impressive run to the last four of the World Cup. Contepomi, a flyhalf for Leinster who has played a key midfield role alongside Hernandez, is the tournament's second highest scorer with 64 points in the Pumas' five victories.
"The IRB Player of the Year Award is the ultimate accolade for a player to receive in his career. It takes on added significance in a Rugby World Cup," said International Rugby Board chairman Syd Millar. "The list of past winners of this prestigious award is very impressive and comprises players of the calibre of Schalk Burger, Dan Carter, Jonny Wilkinson, Richie McCaw, Fabien Galthie and Keith Wood."
The inclusion of Argentina in a major annual international competition such as the Six Nations or the Tri-Nations is an issue the IRB has said it is looking into. The Pumas face South Africa in Sunday's semi-final at the Stade de France.
"[Argentina] have given southern hemisphere teams very hard games, it's been the same in Europe, so there's nothing surprising about it," Millar said of the Pumas' success at the World Cup.
"They've got players in Europe playing at a very high level. They're in the right position that they deserve," he added of Argentina's ranking at number four.
France leapt into second place in the international rankings following the 20-18 World Cup quarter final victory over top-ranked New Zealand.
South Africa remain third and Argentina fourth ahead of their semi-final at the Stade de France on Sunday. England stay in sixth despite beating the Wallabies, on account of a terrible record since winning the World Cup in 2003.
Ireland, Scotland, Fiji and Wales are the other teams in the top 10.