The Gunners have had two bids rejected for the Gabon international this month but it is understood they are now close to agreeing a fee with Dortmund.
Arsene Wenger is believed to be confident of securing Aubameyang's signature, with Arsenal expected to pay the Bundesliga club around £60m.
The deal will make the 28-year-old the Premier League club's most expensive ever signing.
Dortmund are understood to have already lined up a replacement - former Blackburn Rovers man Anthony Modeste - and will sanction Aubameyang's exit once they bring in a new striker.