Giroud has just six months remaining on his contract at Stamford Bridge and could leave for free at the end of the season.
The 34-year-old France international has attracted interest from Italian champions Juventus, whose manager Andrea Pirlo recently declared interest in the world cup winner.
Giroud has not always been first choice during his time at Chelsea but has rarely let his team down when called upon.
The former Montpellier striker has scored nine goals in 15 appearances across all competitions this season despite jostling for a starting berth with Tammy Abraham and Timo Werner.
Despite the uncertainty surrounding his future, Giroud is not looking for an exit in the January transfer window.
"The ambition is to win something with Chelsea this season. The rest of my career, in the short term, I see it at Chelsea. Now we know that things are going very quickly in football, for good and bad [reasons]. I want to keep a cool head and concentrate on the pitch,” the former Arsenal striker told French publication Le Dauphine Libere.
"My contract at Chelsea will end in June, even though I have the option to stay for another year. We will discuss it at the end of the year.
"But, once again, I have the ambition to win something with Chelsea this season because I have high hopes linked to the quality of our squad."
