Tottenham left winger Bale and Arsenal midfielder Nasri are the favourites to land the award for their early season performances.
Also nominated are Scott Parker, Rafael van der Vaart, Charlie Adam and Carlos Tevez.
Nemanja Vidic also makes the shortlist.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.