The 32-year-old told RMC Sport (h/t Julien Laurens at ESPN FC) that he could be tempted to head for North America in the future.
"MLS, for my family, my children who speak English...it is interesting," he said. "In a year? Two years? I don't know when. But of course, I will be opened to a new challenge. It is not only MLS which could interest me."
Giroud was linked with a move away from Chelsea in the summer transfer window. Ligue 1 sides Nice, Bordeaux, Marseille and Lyon were all interested in the striker, per Metro.
However, the France international also said in the interview he had not seriously considered leaving the Blues in the summer, per Laurens.
"There has been no discussions because the club had an option for an extra year, and they took it because they were happy with my contribution to the club. It is even more than that. There is real trust. It was not really my desire to leave anyway, so I never asked myself about a possible departure."
The longtime Arsenal player opted to sign a one-year contract extension with Chelsea in May after a strong season:
Giroud managed 13 goals in all competitions for Chelsea as the team finished third in the Premier League and claimed the UEFA Europa League. The Frenchman played a key role in their European triumph and was the tournament's top scorer with 11 goals.
Chelsea were unable to add to their attacking options over the summer due to a transfer ban, but Giroud faces competition for a place in the starting XI this season from Tammy Abraham.
The 21-year-old spent last season on loan at Aston Villa but has already made an impact back at the Blues with four goals in four appearances:
Giroud will have decisions to make at the end of the season about his future. He will be available as a free agent unless he signs another contract extension, but he may not want to remain at the club unless he is guaranteed regular football.