The players are both Puskas award nominees for their stellar goals in the past 12 months, alongside the likes of Nemanja Matic and Antonio Di Natale.
As part of the buildup to the annual Ballon d'Or ceremony, 10 of the top strikes from the past 12 months are available for soccer fans to choose from, with the options to be whittled down to the three most popular Dec. 9.
Neymar gets the nod for his strike for Brazil against Japan at this summer's Confederations Cup, and he could become the first player to win the award twice.
Sweden forward Ibrahimovic is also on the list for his outrageous overhead kick from more than 25 yards out against England in a friendly last November.
The only major European league on the list is Serie A, which has two entrants: Antonio Di Natale for an acute volley in Udinese's clash with Chievo in April and Bologna's Panagiotis Kone with his acrobatic, twisting volley against Napoli.
Juan Manuel Oliveira capped off some fine one-touch Nautico passing with a stunning volley versus Sporting Recife to earn a nomination, while Pachuca midfielder Daniel Luduena gets his spot for having the audacity to shoot and score from beyond the halfway line.
Peter Ankersen's entry has shades of Marco van Basten's famous volleyed finish in the 1988 European Championship final, though Nemanja Matic's sweetly struck goal from outside the box could sway voters.
There are also two female entrants: France's Louisa Necib for her long-range strike and Australian player Lisa De Vanna - who struck a superb overhead kick inside the 18-yard box.
The winning goal will be announced at the Ballon d'Or ceremony on Jan. 13.