The 22-year-old midfielder has scored five goals in seven top-flight appearances this season, including one in the Gunners' 4-1 victory over Norwich City at the Emirates Stadium on Sunday.
"Aaron is doing incredibly well," Vermaelen told The Mirror. "He showed it again against us [Belgium] in midweek with his goal. He is the best player in the Premier League at the moment.
"He is scoring goals and looking really sharp with his passing. He's doing extremely well. He's been unbelievable for us.
"He got the Player of the Month award, scoring goals, playing well and showing he is important for us. There is more to come from him because he is young."
Arsenal are currently top of the Premier League, having picked up 19 points from seven games.