The 30-year-old has faced an uncertain future this summer after the Gunners made clear their intentions to invest heavily in the transfer market and have already completed the club-record capture of Alexandre Lacazette from Lyon.
As a result, a number of clubs have expressed an interest in his signature, including the French south coast side and big-spending Premier League side Everton.
Speaking to L'Equipe about the Frenchman's situation, Garcia conceded: "I do not think he wants to come to Marseille, Olivier Giroud. That's the problem.
"It is understandable - as he is a striker with the French national team who is making progress with Arsenal - that when he does change clubs, his interests might lie beyond OM."