The club have allowed the striker to travel overseas after agreeing terms with Dortmund, in a deal that could include an option to buy after an initial six-month loan, but sources close to Chelsea have reiterated that Batshuayi will not be leaving without Giroud heading to Stamford Bridge.
The France striker netted 105 goals in 253 appearances during his time with us and won the FIFA Puskas Goal of the Year for his scorpion kick last season.
Arsenal midfielder Mesut Ozil has signed a new three-and-a-half-year deal to stay at the club until 2021.
The 28-year-old, who scored 98 goals in 144 Bundesliga games for Dortmund, is a replacement for Alexis Sanchez following his switch to Manchester United.
Aubameyang had been in dispute with Dortmund in recent weeks as the tried to push through the transfer but the German club's sporting director Michael Zorc has wished the striker well in North London.
However, this would also see Olivier Giroud leave for Chelsea and the Blues would then be free to let Michy Batshuayi go to Dortmund.
Aubameyang will become Arsenal's record signing, and is famed for his electric pace and lethal finishing ability.
Aubameyang will link up with former Dortmund teammate Henrikh Mkhitaryan after the Armenian joined Arsenal as part of the Sanchez deal.
However, despite these reports, Giroud still came off the bench during our 3-1 defeat at Swansea last night and Wenger insisted after the game that a final decision over the Frenchman's future hadn't been made yet.
The 24-year-old, who represented his country at Euro 2016, hopes regular first-team action will help his chances of featuring more prominently at this year's World Cup in Russian Federation.