The Norwegian star had been tipped as one of football's most promising young talents when he joined Real Madrid as a teenager but is yet to make the desired impact and has joined Arsenal on loan, with Gunners boss Arteta backing him to live up to the hype.
The Spanish coach said: "Well, he’s got the potential [to be one of the best]. I followed him very closely when he was at Real Sociedad and he was really impressive over there for long periods.
"He had a really successful season over there and that’s one of the reasons why I was so convinced that he’s a player for us. He’s a player that I really like and, as you say, still has huge potential to become even better."
Odegaard has featured on a number of occasions in the early stage of his Arsenal career and Arteta is pleased with the way he has begun his spell with the Premier League club.
He said: All positive from my first conversations with him. He’s a really focused and humble boy that was really keen to join.
"He’s a really nice guy, the players like him, the staff like him, he’s easy going, a really hard worker and I’ve been very impressed with his leadership. He looks a little bit calm but on the pitch he’s got something about him."
Arteta also lauded Odegaard for his leadership and intelligence during matches.
He said: "When I talk about leadership, it's how he talks to his team-mates, how he commands the high press and then the personality he shows.
"Every time the opponent comes after him, he still shows for the ball in the right areas. His decision making is really good and he's a really intelligent player."