Aubameyang is wanted by Manchester City this summer with Pep Guardiola keen on the striker.
But the Gabon star looks set to snub City with Watze claiming that no one but Spain's big two could attract him from Dortmund.
Dortmund CEO Watze told Sport1’s Doppelpass: “I think he will stay with us. But if Real Madrid or Barcelona come along with an offer, maybe he’ll think about it.
Pierre-Emerick Aubameyang is only ready to swap Dortmund for one of Spain's big two
Pierre-Emerick Aubameyang is preparing for tonight's game with Monaco
“The rest of the clubs who are interested in him are not really an alternative for him.
“And certainly not Bayern (Munich) because we wouldn’t allow him join them.”
Chelsea and Man Utd stars make Pierre-Emerick Aubameyang's dream XI Tue, March 14, 2017
Pierre-Emerick Aubameyang has named his dream XI made up of team-mates and opponents, with Chelsea and Manchester United players featuring heavily
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Pierre-Emerick Aubameyang has named his dream XI from opponents and team-mates
Aubameyang, 27, starts for Dortmund in the Champions League quarter-final against Monaco tonight.
He has scored 32 goals for the Bundesliga side this season and is under contract until 2020.
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