The club's general manager Hans-Joachim Watzke is adamant the Gabonese striker, who has hit 25 Bundesliga goals this season, will not become the latest Dortmund star to swap Signal Iduna Park for the Allianz Arena.
Robert Lewandowski and Mats Hummels are among the high-profile players to have switched from Dortmund to Bayern in recent years, but Watzke said Aubameyang would only be allowed to move to Barcelona or Real Madrid.
"I think he will stay with us," Watzke told Sport1. "But if Real Madrid or Barcelona come with a big offer, then we have to discuss it.
"We will not sell him to the Bavarians."
Speculation about Thomas Tuchel's position at the club intensified following Dortmund's 4-1 Klassiker loss to Bayern on Saturday, but Watzke shrugged off reports about the coach's future, despite Dortmund sitting fourth in the Bundesliga table.
"I do not see that we have irreconcilable differences and there is no thunderstorm," Watzke added.
"We have not even thought about alternatives."