Giroud's future at Emirates Stadium has been the subject of considerable speculation during the close season following the arrival of Alexandre Lacazette from Lyon.
Arsene Wenger splashed out a club-record fee, thought to be in the region of €53 million, for Lacazette last month and he has been first choice as Arsenal's lone central attacker in their pre-season friendlies.
Lacazette was also given the nod in the Community Shield against Chelsea last weekend, although it was substitute Giroud - having replaced Lacazette - who scored the winning penalty to secure a 4-1 shoot-out win following a 1-1 draw at Wembley.
With Danny Welbeck and Theo Walcott also vying for the role of centre-forward, chances for Giroud could be limited in 2017-18, and that has led to speculation he could return to France.
Marseille have been one club heavily linked with the 30-year-old, but Garcia says the France international is not interested in a move to the Stade Velodrome.
"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.
"It also shows that we have steps to take in order to be attractive [to players]. Today we are still a little short [of appealing to top players].
"I do not know which forward we will get to come, but I hear a lot of things, and you do not want people to dream and think we're going to sign a top player.
"We cannot afford it."