Dortmund have now rejected second offer from Arsenal, according to multiple sources and also reported by the BBC
The new offer on Wednesday was below the valuation of Dortmund which is believed to be in excess of £50m.
The latest round of negotiation did not include a player going the other way.
There has been suggestion that Arsenal may be willing to offer Giroud on loan till the end of the season, as Dortmund may not be willing to sell without a replacement and Giroud may also be opened to the chance of a regular playing time to have a chance of being included in the French National team squad to the World Cup later this year.
Arsenal is expected to decide what to do from this point, the Window closes in 6 days time, and so have very little time to commence a new negotiation with an alternative forward, meanwhile, failure to bring in a capable replacement for Sanchez may cause further fans unrest.
The club is still being linked with West Brom defender Jonny Evans which is unlikely to be concluded until the Aubameyang deal finalised.