The Gunners are said to be increasingly confident of signing the 28-year-old this month as they look for replacements for Alexis Sanchez and Theo Walcott, who have been tipped for respective moves to Manchester United and Everton.
Aubameyang has fallen out of favour at Dortmund amid the speculation, with the club's sporting director Michael Zorc today claiming that the player's "behaviour" is reaching "a point where you can no longer tolerate it".
According to The Sun, Arsene Wenger's side are reluctant to meet Dortmund's £60m valuation of Aubameyang and will instead make an offer of £30m plus the services of Giroud, who remains down the pecking order at the Emirates.
The newspaper also claims that Arsenal will not sign both Aubameyang and Bordeaux winger Malcom, who has been linked with a £45m switch to North London, and will make the former their "priority" this month.
Aubameyang has been in lethal form for Dortmund in recent seasons and had a hit-rate of 13 goals in 15 Bundesliga appearances in the first half of the campaign.