Aubameyang, who scored 31 goals in the Bundesliga last season, has been linked with big-money moves to Real Madrid, Chelsea, AC Milan and Paris Saint-Germain in recent weeks.
The 28-year-old netted twice on Tuesday as Dortmund beat AC Milan 3-1 on their pre-season tour of China.
The transfer window in Germany closes at midnight (2200 GMT) on August 31, but director of sport Michael Zorc claimed it is effectively already shut for Aubameyang.
“We have decided that ‘Auba’ will stay with Borussia Dortmund. The transfer window is closed as far as he is concerned, because otherwise we would have run out of time (to find a replacement),” insisted Zorc.
Chinese side Tianjin Quanjian had also reportedly wanted to pay 80 million euros ($92.6m) for him, but with three years left on his Dortmund contract, the German club says Aubameyang is staying put.
New coach Peter Bosz, who has replaced Thomas Tuchel, unsurprisingly would want Aubameyang at Dortmund when the Bundesliga season starts on August 18.
“I am glad that he is in my team,” said the Dutchman.
“He is an extraordinary player and he has shown that once more against Milan.
“He’s a great bloke and a great footballer.”
Last weekend, Dortmund’s managing director Hans-Joachim Watzke had said they expected Aubameyang to stay: “We are waiting a few more days, but we will not have to wait long.”