Giroud has fallen down the pecking order at Arsenal following the club-record £52million arrival of striker Alexandre Lacazette.
The France international travelled with the rest of the Gunners’ squad for their pre-season tour of Australia.
But Giroud, who is wanted by Everton, West Ham, Marseille and AC Milan, has revealed he may quit Arsenal.
Speaking at the launch of the club’s new dark grey third kit in Sydney, he said: “It (leaving) is an option to be honest with you.
“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.
“But it is true that I really enjoyed my five years with Arsenal. 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.
“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.”
Giroud has never managed 20 goals in any of his five seasons at the Emirates since joining from Montpellier for £9.6million in 2012.
Arsene Wenger has insisted he does not want Giroud to leave with Arsenal likely to ask around £35million from any interested parties.
Olivier Giroud may have played his last game for Arsenal
The Mirror say Everton have been leading the chase but Marseille believe thay can tempt him back to his homeland.
Giroud knows he needs to play regular football this season to keep his place in Didier Deschamps’ squad for the 2018 World Cup.
But the 30-year-old is not afraid of battling Lacazette for a spot up front if he does stay in north London.
“It’s always nice for the club to get several strikers with different qualities and it is always nice for competition and it helps you to step up every time,” Giroud added.
“I really enjoyed all my time at the Arsenal and I scored a few nice goals but always like to speak about the team, the team spirit and the team work.”