Wenger is pleased with the progress the striker is making in his debut season in the Premier League, and sees similarities with an Arsenal legend.
"[He is] maybe like Alan Smith, a little bit - he can develop into this kind of player," the manager said.
"Our fans like Olivier Giroud, because he is a guy who is developing very well. First of all he fights for the team, he has great qualities and charisma. I am convinced there is a lot more to come from Olivier and that he can convince our fans he is the striker they look for.
"It always takes time, but he has scored 11 goals and has many assists. He is strong in the air, defensively and offensively, and overall he has important qualities for the team."