Giroud strongly considered an Arsenal exit when it became clear France team-mate Alexandre Lacazette's club-record arrival in July would eat into his starting opportunities.
But he ultimately opted to remain with the Gunners and passed 100 goals for the club in last month's Europa League victory over BATE.
Giroud said to Canal Plus: "I had the opportunity to leave. I was very close to another English club - Everton - but I think I made the best choice.
"I have a lot of respect for Marseille, I was a fan for years. I also have a lot of respect for Lyon, who were also interested at one time.
"I'm happy in England, it's nothing against those clubs, I didn't want to return to France. But a return to France is possible one day."
After the transfer window, Giroud said he had rejected an exit because his "story is not finished" at Arsenal.
Giroud is yet to start a Premier League game for Arsene Wenger this season, but has come on as a substitute in all seven of their matches.
Everton, meanwhile, only have four goals in seven league games this season as they struggle without Romelu Lukaku.