The striker's contract at Stamford Bridge is poised to expire at the end of the current campaign, having joined the Blues on an 18-month deal in January 2018.
Following the arrival of Gonzalo Higuain in the previous window, Premier League appearances have been rare for Giroud, albeit he has shone in the the UEFA Europa League.
The France international has said he wants to be at a club where he has a more significant role and was asked specifically about Lyon, who have been mentioned as possible suitors, per Foot Mercato (h/t Goal):
"Lyon was mentioned because the president talked about it. I know what he is saying and I am very happy with the interest of some French clubs in my regard.
"It's a club with very good young players, very good players, a very good staff. On the international scene, we saw good matches from Lyon against [Manchester] City, or against Barcelona, even if the return was more difficult. ...
"I do not disrespect the attackers already there, including the young [Moussa] Dembele who has produced some great performances. I also know that, in Lyon, they talk about certain departures. Of course. I want to become important again, with the confidence of a coach."
Speaking to RTL (h/t Get French Football News), Giroud said since Higuain's arrival he feels "there is no competition."
Following the arrival of manager Maurizio Sarri, the former Arsenal man was used sporadically in the Premier League, often jostling with Alvaro Morata for a starting spot. But after Higuain's loan move and Morata's loan exit, his starts appear to be exclusively limited to the Europa League.
In his previous outing in that competition, Giroud netted a hat-trick in the 5-0 demolition of Dynamo Kiev (UK only):
It was a treble that saw his goal involvement in Europe reach double figures, having notched nine goals and one assist:
The 32-year-old may lack speed and explosiveness, but when he does start matches for Chelsea, he rarely lets the team down.
What he doesn't have in dynamism, he makes up for with smart hold-up play, aerial power and sharp instincts in the penalty area. He's been a useful acquisition for Chelsea, and as a back-up striker, he's one of the best in the division.
Given Higuain hasn't caught fire since his switch to Stamford Bridge, Liam Twomey of ESPN FC thinks Giroud could get more starts:
Even so, the player's desire to get more game time is understandable. Not only will he want to be making the most of the remaining years of his career, he will be keen to remain in contention for the France squad for manager Didier Deschamps.
With that in mind, at this point his future does appear to be away from Chelsea. Whichever club does land Giroud will be securing the services of a striker who still has plenty to offer.