According to German publication Bild, the Gunners have raised their original offer of £48.3m to £50.9m.
It has been reported that Dortmund are holding out for £61.5m.
Arsenal have sent a negotiating party to Germany that includes chief executive Ivan Gazidis, head of recruitment Sven Mislintat and contract negotiator Huss Fahmy.
Talks are still ongoing and speaking on Tuesday, manager Arsene Wenger remained coy when asked about the transfer.
"Confident or not confident, I don't know," he said. "You never know how close you are.
"This is the kind of thing - he is one of the possible movements, but we have other things in mind as well. We have plenty of opportunities and the final decision is not made.
"At the moment we are not close to any deal, Aubameyang or anybody else."