Everton had sent the 20-year-old out on loan to the Belgian champions for the season, but their attacking struggles have led to Ronald Koeman's side considering recalling the youngster.
Giroud joined Arsenal from Montpellier after Euro 2012 to replace Robin Van Perise who left to join Manchester United.
But Giroud, 31, believes he made the right decision to turn down Everton in favour of remaining with the north London side.
Giroud recently scored his 100th goal for Arsenal during a Europa League fixture against Bate Borisov several weeks ago, becoming only the 19th Arsenal player to do so.
"But I made the best choice I think".
He added: "I have a lot of respect for Marseille, I was a fan for years".
'I was very close to another English club, Everton.
'I also have a lot of respect for Lyon, who were also interested at one time.
Giroud has managed 2 goals in 10 games for the Gunners so far this season, though all 7 of his appearances in the Premier League have come from the bench.
They now sit six points behind leaders Manchester City after seven games of the new campaign as they prepare for their trip to Watford in the Premier League on Saturday afternoon. "But a return to France is possible one day". I didn't want to return to France.
With Giroud hoping to make France's squad for the 2018 World Cup, he will have to make a bigger impact as the campaign progresses.