The 28-year-old has helped his side go five points clear of champions Bayern Munich at the top of the Bundesliga, finding the net 13 times in all competitions so far this season.
The Gabon international, who was named on the 30-man Ballon d'Or shortlist, was heavily linked with a move away from the Bundesliga in the summer but says that he is happy at his club.
"I have always felt very comfortable in Dortmund, in the team and at BVB, and that is true today, too," Aubameyang told Bild. "BVB is my family!".
The league leaders will be looking to continue their excellent start to the season when they host fourth-placed RB Leipzig on Saturday.