Giroud admitted his Arsenal future is in doubt following the Gunners' acquisition of Alexandre Lacazette, but it remains unclear if Dortmund would be willing to meet the valuation.
Arsenal forward Olivier Giroud has emerged as a potential signing for Borussia Dortmund if star striker Pierre-Emerick Aubameyang leaves the club this summer.
Aubameyang has long been linked with a potential switch to the Chinese Super League, with a mega-money offer from Tianjin Quanjin thought to be on the table, but with the Far East club said to be close to pulling out of a deal amid fears he wants to join Chelsea, Europe's elite have been alerted to his availability.
AC Milan are also planning talks with the Gabon international, with Dortmund thought to be eyeing Giroud as a potential replacement.
Olivier Giroud has emerged as a potential transfer target for Borussia Dortmund
Giroud would be an option if Pierre-Emerick Aubameyang leaves Dortmund this summer
The French striker has admitted his Arsenal future is in doubt following the Gunners' club-record acquisition of Alexandre Lacazette, but it remains unclear whether Dortmund would be willing to meet Arsene Wenger's valuation of the 30-year-old.
Everton have a continued interest in the France international but are not convinced he sees them as their first choice, with AC Milan, West Ham and Marseille also keen.
Giroud, who signed a new three-year deal at Arsenal in the summer, even referred to his Arsenal career in the past tense while speaking during the club's pre-season visit to Australia.
Giroud has admitted his five-year Arsenal career could be coming to an end
Aubameyang remains a target for Chelsea, AC Milan and Chinese side Tianjin Quanjin
'It (leaving) is an option to be honest with you,' he said.
'I'm here in pre-season, I wanted to travel. Some people asked me if I am going to travel or not and of course, I am Arsenal player and for the moment I am here so I just want to prepare well for the season and we will see later.
'It is true that I really enjoyed my five years with Arsenal,' Giroud added. 'I'm still an Arsenal player for the moment so I try to be professional. No matter what happens, I did my job on the pitch.
Arsenal Giroud during the unveiling of the Gunners' new third kit in Sydney
'It's been five years that I've been here. It could be my sixth one. I had an amazing welcome from the fans and from the club and it has been five amazing years for me.
'I won't forget it, no matter what happens. We will see about my future but I am still an Arsenal player for the moment.'
Arsenal faced Sydney FC in their opening game of their Australian swing on Thursday, with Giroud and Lacazette starting the match on the bench.Read more at dailymail.co.uk