The 30-year-old penned a new deal earlier this year keeping him at the Emirates until 2019 but found game time hard to come by last term, making just 11 starts in the Premier League.
The club-record arrival of Alexandre Lacazette from Lyon and manager Arsene Wenger's continuing pursuit of AS Monaco hotshot Kylian Mbappe has led to increased speculation over his future, with Marseille and West Ham United thought to be waiting in the wings with offers for the Frenchman.
Asked about his future during the Gunners' pre-season tour of Australia, Giroud admitted: "Honestly for me I don't know. For the moment I'm still an Arsenal player so I try to be professional and prepare well for the next season."
Quizzed on whether he was worried that Lacazette's arrival would further limit his opportunity, he responded: "Obviously there will be more competition, even more than the last year, but it's always nice for a striker to feel the pressure. I always deal with it."
Giroud has been with Arsenal since 2012 and has a record of 98 goals in 226 appearances, including 69 in 164 in the Premier League.