The 20-year-old, who won the award last year having also been nominated in 2010, is on the 10-man shortlist for his individual effort for Santos against Internacional on March 7, where he picked up the ball in his own half and evaded the attentions of three opponents before netting.
Neymar's fellow global superstar Lionel Messi is also in the running for the third successive year with his effort for Argentina against Brazil, while Atletico Madrid striker Radamel Falcao and Mexican women's international Olivia Jimenez also feature in the race for the award.
Ben Arfa owes his place on the 10-man shortlist recognising the best goal of the year to his strike in Newcastle's FA Cup win over Blackburn on January 7, when he went on a mazy run before cracking a fierce shot high into the Rovers net.
The shortlist will be reduced to three when a first round of public voting on FIFA's website ends on November 29, and the award, in honour of Hungarian great Ferenc Puskas, will be handed out at the Ballon d'Or gala on January 7, 2013.
Puskas Award nominees:
Agyemang Badu - for Ghana against Guinea, February 1
Hatem Ben Arfa - for Newcastle against Blackburn, January 7
Radamel Falcao - for Atletico Madrid vs America de Cali, May 19
Eric Hassli - for Vancouver Whitecaps vs Toronto FC, May 16
Olivia Jimenez - for Mexico vs Switzerland, August 22
Gaston Mealla - for Nacional Potosi vs The Strongest, January 29
Lionel Messi - for Argentina vs Brazil, June 9
Neymar - for Santos vs Internacional, March 7
Moussa Sow - for Fenerbahce vs Galatasaray, March 17
Miroslav Stoch - for Fenerbahce vs Genclerbirligi, March 3