The Bundesliga side are set to play Hertha Berlin on Friday.
According to Bild, manager Peter Stoger has given the Gabon international time off to seal a move to the Gunners.
With star forward Alexis Sanchez seemingly on his way to Manchester United, Arsene Wenger has acted rapidly in finding a replacement.
Dortmund value Aubameyang at £60m and as the player has agreed personal terms, the only factor remaining is for the two clubs to agree on a transfer fee.
Aubameyang's father, who also acts as his agent, is reportedly travelling to London for talks with Arsenal.
Dortmund meanwhile reportedly want Chelsea striker Michy Batshuayi as his replacement.
Inside Pierre-Emerick Aubameyang's jet-set lifestyle
Pierre-Emerick Aubameyang
“Disappointment is the wrong expression”
Peter Stoger
The Belgian scored for the Blues tonight as Antonio Conte’s men eventually beat Norwich on penalties in their FA Cup replay.
According to German publication Bild, Stoger has given Aubameyang a leave of absence rather than having an unsettled player around the squad.
“Disappointment is the wrong expression,” the Dortmund coach explained when asked about his feelings towards the player.
“Rather a lack of understanding as I cannot really comprehend his conduct.
“And I am certainly not the only one."
getty
getty
Arsenal were hoping to tempt Dortmund into selling Aubameyang by offering Olivier Giroud in part-exchange for the Gabon international.
But RMC Sport claim that although Dortmund do want to sign Giroud, they will not entertain a swap deal.
The Bundesliga side have warned Arsenal the two deals have no bearing on the other.
Giroud has been linked with a host of clubs this month with West Ham and Everton still interested in his signature.