The prospective move will only go through during the January transfer window if Dortmund can find a replacement, fow24 reports.
Arsenal have seen two bids for Aubameyang rejected already, most recent an offer of 50m euros (£43.64m) on Wednesday.
Aubameyang was left out of Dortmund’s squad to face Hertha Berlin last weekend, though he did play all 90 minutes in Saturday’s 2-2 draw with Freiburg.
"We are ready to realise a transfer under certain parameters but only if these are fully met," Dortmund’s sporting director Michael Zorc told German TV.
"We have a clear position. Arsenal has started several attempts so far. We have up to now refused them all."
Reports suggest a move for Aubameyang will allow Giroud to leave the Emirates, though the Frenchman will not be heading to Germany, according to Sky Sports News.
Giroud is said to be a £35m target for Chelsea, who have been chasing a targetman this January and have already been linked with West Ham's Andy Carroll, Stoke's Peter Crouch and Roma's Edin Dzeko.




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