Spurs and England international Kane has won the individual accolade in two of the last three years, with Liverpool’s Mohamed Salah outscoring him in the previous campaign.
Aubameyang has certainly made a swift start to life at Arsenal following his £56m move from Borussia Dortmund, scoring ten goals in 14 appearances across all competitions.
Parlour believes the Gabon international will be a key player in the upcoming season and can see him rivalling Kane for the Golden Boot.
Speaking to bwin, Parlour said: “Aubameyang will be Arsenal’s star player this season.
“He has that incredible goalscoring instinct and he’ll get lots of opportunities with (Mesut) Ozil and (Henrikh) Mkhitaryan feeding him."
Parlour continued: "I was so impressed with what I saw last year that I think it will be him and Harry Kane competing for the Golden Boot."
Kane has become recognised as one of the best strikers in the world and will have no intention of dropping his standards anytime soon.
The 24-year-old has already chalked up 140 goals in total during his Spurs career and is five years younger than Arsenal counterpart Aubameyang.
Kane has just guided England to a fourth-place finish at the World Cup and walked away with the tournament’s Golden Boot with six goals, while Aubameyang has had a full pre-season to prepare with Arsenal.