Gedion Zelalem has already made his Champions League debut against Borussia Dortmund
The young midfielder looks an exciting prospect and has already made his senior debut in the FA Cup against Coventry in 2014.
However, Gazidis has warned that too much pressure on his young shoulders could damage his future development.
He told Sports Illustrated: "You have to temper this [expectation] because you are always looking for the next big star, and I've been guilty of this myself.
"Gedion is an exciting young talent, he's got German heritage, and speaks like an American kid.
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There's something exciting there, but lets not get things ahead of themselves
Ivan Gazidis
"Right at this moment he's not the finished product. He's very much got a lot of development to do.
"He's focused on doing that. There's something exciting there, but lets not get things ahead of themselves."
Zelalem made his Champions League debut this season, getting 45 minutes under his belt in the home clash with Borussia Dortmund.
But the midfield man has mainly been restricted to U19 and U21 action, contributing one goal and one assist in six appearances for the Gunners' under 19s.
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