The bid of 50m euros (£43.64m) was made by the Premier League club on Wednesday and was turned down immediately.
It is understood Dortmund will only consider selling the Gabon forward, 28, for a fee in excess of £50m.
It has previously been suggested Arsenal would include Olivier Giroud in any deal but Wednesday's bid was purely a cash offer for Aubameyang.
The Gunners must now decide whether to pursue their interest in the forward or, with only a week of the transfer window remaining, pursue alternative targets.
Aubameyang has been targeted by Arsenal during the current transfer window and a deputation from the club flew out to Germany to meet with their Dortmund counterparts last weekend.
Aubameyang has twice been dropped for disciplinary reasons this season and was not selected for the draw at Hertha Berlin on Friday.
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