Giroud, 31, was linked with a move away in the close-season but instead ended up staying at Arsenal.
But the France international is yet to make a Premier League start this season, scoring just once in 10 appearances as a substitute.
Giroud, who netted for his nation in a 2-0 friendly win over Wales on Friday, said he was still happy with his decision to remain at the Emirates Stadium.
"For the moment I am not questioning myself about my future," he told UK newspapers.
"I am happy at Arsenal and I am fine with the decision to stay because I want to. I am thinking that the story between the club and myself is not over and not finished.
"I keep believing in my quality and I keep the faith. I have a lot of objectives with Arsenal and my country so I always try to move forward and keep scoring."
Giroud has scored twice in four Europa League starts, but his record of having netted at least 10 league goals in each of his seasons with Arsenal could be coming to an end.
However, the striker said he trusted Arsene Wenger, and he was keen to repay his manager when possible.
"Arsene's always supporting me and there is a lot of trust in each other," Giroud said.
"He trusts in me and I try to give it back on the pitch when I can."