The Gunners have been chasing the Gabon international all month after Alexis Sanchez left to join Manchester United.
Arsenal had two bids initially turned down believed to be in the region of £50m.
However, it now appears they have agreed terms with the Bundesliga outfit for a fee of €63m (£55m).
That is according to German publication Kicker.
It is also reported that Olivier Giroud will not be moving in the opposite direction as he prefers a transfer to Stamford Bridge.
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The report is reiterated by German football expert Manuel Veth who wrote on Twitter: “Movement in the #Aubameyang to #Arsenal deal.
“@kicker believes that the #BVB striker will be sold for €63m.
“Giroud will not head to Dortmund instead the club is looking at Anthony Modeste as a potential replacements.”
And when asked how reliable his information was, he replied: “very.”
Alexandre Lacazette is Arsenal’s current record signing at £52m.
However, the honour will now belong to Aubameyang once the move is completed before the deadline slams shut on January 31 (11pm).
Personal terms are still yet to be agreed but it is believed that it should be simple given the player’s desire to move to north London.
Chelsea will also be handed a boost by the news at it would mean Giroud would now be available to move to Stamford Bridge.