'Sky Germany' reports that the Frenchman's name has come up as discussions continue between the two sides over Aubameyang.
Arsenal chief executive Ivan Gazidis and head of recruitment Sven Mislintat are both thought to be in Germany as Arsenal look to thrash out a deal for the Gabonese.
However, as things stand, no fee has been agreed between the two parties.
Arsenal hope that including Giroud in the deal could help them lower the asking price for Aubameyang, with Dortmund thought to be holding out for well in excess of £50m for their star man amid reports that they rejected a £44m offer on Sunday.
The French international has started just one game in the Premier League so far this season, having fallen down the Arsenal pecking order following the arrival of compatriot Alexandre Lacazette.
The move is thought to appeal to Giroud, who is aware of the need to feature more regularly in the second half of the season as he looks to ensure a place in the France squad for this summer's World Cup.