The Premier League club have already reached an agreement on personal terms with the Gabon striker, and are locked in talks over a fee with BVB.
But so far their offers have fallen short of what the Bundesliga side want for their star, who was left out of their weekend clash against Hertha Berlin.
The Gunners have already tabled two bids, worth €50 million and €58m, which have been rejected.
Dortmund are holding out for €70m, but could compromise on a deal worth €65m if negotiations continue to drag, while Arsenal remain confident of striking a deal.
Olivier Giroud could also enter the equation as a loan makeweight in the deal, with Dortmund keen to replace Aubameyang with a proven striker before the end of the window.
While BVB are keen, however, Arsenal are more reluctant to agree to a temporary switch, unless Giroud's presence in the offer allows them to reduce Aubameyang's fee.
"Anything can happen in the next few days," a source close to Giroud explained to Goal.
"The only concrete point we know is that Dortmund really aren't agreed on Arsenal's offer. And that makes for a lot of consequences."
As previously reported, West Bromwich Albion defender Jonny Evans is also a target at the Emirates Stadium, although Aubameyang is the club's top priority.