The striker, who recently scored his 100th goal for the Gunners, was the subject of serious interest from Ronald Koeman's side.
He was also being targeted by West Ham and French clubs Marseille and Lyon, but Giroud believes he made the right decision to stay in North London.
"I had the opportunity to leave [Arsenal]," he told French TV station 'Canal Plus'.
"I was very close to another English club, Everton. But I think I made the best choice."
Giroud also admitted that he is not ready to move back to a Ligue 1 club just yet.
'I have a lot of respect for Marseille, I was a fan for years,' he said.
'I also have a lot of respect for Lyon, who were also interested at one time. I didn't want to return to France.
'I'm happy in England, it's nothing against those clubs. But a return to France is possible one day.'