Aubameyang handed in a transfer request recently after having his head turned but the Gunners.
Despite Dortmund denying talks have been held between the clubs, it's believed negotiations are at an advanced stage.
The Gabon international striker was left out of the Bundesliga club's match against Hertha Berlin on Friday.
All signs point to a deal on the verge of being reached between the two clubs.
And now it's emerged that Giroud could replace Aubameyang at the Westfalenstadion until the end of the season.
Giroud has played second-fiddle to new signing Alexandre Lacazette through out the season.
The most goals scored as a substitute in one Premier League season
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“Character can be a very positive note and a very negative note”
Arsene Wenger
The French striker has been restricted to starting almost exclusively in cup competitions.
Dortmund's sporting director Michael Zorc admitted the 28-year-old's head had been turned by Arsenal's interest in him.
"He’s practicing in Dortmund," said Zorc. "We felt, that he is not a 100 per cent with his mind focused.
"We’ll see, if this will help him. It’s a difficult situation.”
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Arsene Wenger was quizzed over Aubameyang's supposed attitude problem and asked whether he thought he would fit in at the Gunners.
"Yes, because character can be a very positive note and a very negative note," said the Frenchman.
"I believe overall you look at the player over his career.
"Usually, when a career has been very positive, the character has been used in a positive way."