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The Ukraine international was on Friday announced as Arsenal's new signing after being spotted watching his side's friendly match against Orlando City.
Ahead of his side's Florida Cup match against Chelsea, Odegaard welcomed Zinchenko.
He told reporters: “I’ve seen him play a lot and I really like his qualities, I think he’s a really great player.
“I think he can play both positions, sometimes as a left-back and midfield, I think he can even play as a winger. He can play different positions so I think he will be a great addition to the squad.”
The 23-year-old is also in line to be named the club's captain after taking on the role for much of last season after both Pierre-Emerick Aubameyang and Alexandre Lacazette left.
With no new captain yet selected by Mikel Arteta, Odegaard admits that he wants the role.
He added: “I always enjoy responsibility. I’m captain for my country and it’s a nice experience, so I enjoy that.
“I don’t know anything about the situation here, I think that question is for Mikel and the club, but if he asked me of course I would be happy to do it.”