NEW YORK—Naomi Osaka sees someone special in third-round opponent Coco Gauff.

The world No. 1 says the 15-year-old American phenom reminds her of herself off-court.

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"I mean, off the court she seems like me," Osaka said after her second-round win over Magda Linette. "Well, she seems a little bit more, like, she knows what she's doing. I'm very quiet. I've gotten actually a bit talkative recently, though."

Osaka, who hit with Gauff a couple of years ago, sees a kindred spirit in the American wild card, which is why she approached her to chat in the locker room.

"I saw her in the locker room. She wasn't really talking to anyone," Osaka said. "I was, like, Oh, looks familiar. I'm just going to talk to her. I know she's super young, and I know it's sort of hard to transition. I wasn't even a junior, but I can only imagine as a junior you play these tournaments with your friends, and then you come to the pros and you don't know anyone.

"I was just, like, Oh, she's a really talented girl. I would love for her to come out of her shell a little bit. I just realize that's probably what people say about me, too. Yeah, she's super sweet and I would love to play her, of course. For me, when I hear people talking about someone, I want to have the opportunity to play them just to assess it for myself."

The reigning US Open champion will get the assessment opportunity when the pair face off in what should be an electric match.