Off contract in June, Giroud is being linked with Monaco and Marseille.
And Dugarry told RMC Sport: “I have doubts about his ability to be a Top 10 player in the world. His career shows him anyway: he has a hard time being a member of the big clubs where he plays.
“But he’s a player that counts. He has managed to make a name for himself and he is world champion. Wherever he went, he scored goals. It’s in his genes.
“For Ligue 1? I want to say to him: welcome. It is a call to many French clubs, even all: we must welcome Olivier Giroud. He will score goals all his life, he thinks of the collective and the others.”