The Republic of Ireland international's volley in the 2-2 draw against Bolton Wanderers at Deepdale is one of three goals on the shortlist.
Browne turned to hook a volley over his shoulder into the net from outside the box in the September 1 meeting.
His competition for the award comes from former PNE loanee Adam Reach who is now with Sheffield Wednesday and Aston Villa's John McGinn.
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Reach's goal against Leeds on September 28 has been nominated, as has McGinn's strike in a 2-1 defeat to Sheffield Wednesday.
The shortlist was put together by a judging panel working on suggestions by supporters on Twitter.
But it is a fan poll which will decide the winner - voting is on the SkySports.com until Monday and the result will be announced on Friday, October 26.