The Gunners are reportedly interested in signing the 19-year-old Dutch-Moroccan, who has been capped twice by the Netherlands.
Maher has become a key figure for AZ after making his debut last season, making 18 appearances so far this campaign, scoring five goals.
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A host of clubs abroad including Arsenal and Manchester City have been linked with the attacking midfielder, who can also play in a deeper role, while PSV have been keen on him throughout the winter. However, Verbeek says he would "get the most out of himself" at the Emirates Stadium.
Speaking to Dutch talk show Studio Voetbal, Verbeek said: "I think Arsenal is a perfect club for him. With Arsene Wenger, who worked with young talents like him before.
"He can get the most out of himself at Arsenal. Look at Robin van Persie, he joined Arsenal at a young age and look what he achieved."
Maher was included in the provisional 36-man squad for Euro 2012, failing to make the cut, but made his debut under Louis van Gaal in the 4-2 defeat to Belgium in August 2012.