The France international has come off the bench in all the Gunners' games so far this season having fallen behind club-record signing and compatriot Alexandre Lacazette in the pecking order.
Danny Welbeck also seems to have surpassed Giroud in manager Arsene Wenger's thinking but the 30-year-old striker is likely to get a rare chance to impress from the start in Thursday's Europa League clash with Cologne.
Wenger will make a raft of changes as Arsenal play in the competition for the first time in 17 years, with Giroud expected to be one of several alterations.
Giroud - who scored a late winner on the opening day Premier League win against Leicester - has struggled to hold down a regular first-team place at the Emirates Stadium and admits that he nearly quit over the summer having been linked with the likes of Everton and West Ham.
Asked how close he came to leaving Arsenal, Giroud said: "Actually that's a very private decision because it's true that I was close to leaving the club because I said that I wanted to play.
"But after a big reflection with everybody around me, like my family and my close friends, I (decided I) wanted to stay at Arsenal and I thought the story was not over, (not) finished at Arsenal.
"The club bring me a lot and I think I give it back
I still want to improve again and again and win some more trophies for the club, so as I said to the boss our story is not finished, so everybody was pleased with that."
Wenger has always maintained his desire to keep Giroud - who has 99 goals for the club - at Arsenal and was full of praise for the striker on the eve of the Cologne clash.
"I have said many times that his contribution has been huge," he said.
"He has had a great evolution here and overall (his) contribution has been tremendous, and I think he has shown a very loyal spirit and has a high respect from everybody inside the club, as well as (from) our fans."
While Giroud wants to stay put, full-back Mathieu Debuchy has revealed he was unable to leave during the transfer window despite being told he could depart for free.
He was reportedly set to sign for Nice before the deal broke down and he remains at Arsenal until January at the earliest.
"I don't know what will happen because this summer the coach (Arsene Wenger) would have let me leave without a transfer fee," he told L'Equipe.
"Brighton also enquired in the last few days of the transfer window
But that came to nothing.
"I'm not the future (of Arsenal)
I'm training with the professionals during the week and I am playing with the youngsters at the weekend."
Source : PA