The Ligue 1 side have been persistently linked with move for Giroud this summer to take him back to his homeland from the Gunners.
It is likely that the 30-year-old will consider his options this summer following the big-money arrival of Alexandre Lacazette to the club.
Everton have been linked with a £20million move to keep the striker in the Premier League, and there has been interest from abroad.
Marseille have been strongly linked but Garcia is not optimistic about the switch.
"I think he [Giroud] does not want to come to Marseille," Garcia told L'Equipe. "That is the problem.
"It can be understood, when you are the striker of the French [national] team, that he's eventually going to change clubs, but he may have other interests than OM. We need people motivated to play in our country."