Rosicky turned 33 today, three months into his eighth season with the Gunners following a switch from Borussia Dortmund in 2006.
Wenger told the club's official website: "First of all I believe he is a real Arsenal man because he is here for a long time.
"He is really a football player who presents the way we want to play football, because he's a team player who has pace, has a quick brain, understands the game well. I always like to have him in the team because of all these qualities."
Rosicky returned from a month on the sidelines to start in Tuesday's 2-0 victory over Napoli in the Champions League, playing just shy of an hour in a wide left role.