Kyrgios looked in good form on Monday as he beat Italian Lorenzo Sonego in the first round.
And should the Australian reach the third round, he could set up a showdown with Novak Djokovic.
But first, he needs to get past Khachanov, who lost in the semi-finals of the Rogers Cup last week.
“He’s an amazing player. So young. We played juniors together,” Kyrgios told reporters.
“He’s had an amazing career so far, and he’s going to be one of the best players in the world for a long time. He plays super-aggressive.
“Unbelievable first serve. Great forehand. He’s a big guy, as well. Moves well.
“I’m going to try to keep things on my own terms, but again, I’m not going to think about it.”
Against Sonego, Kyrgios was at his showman best as he delighted the crowd with his tweeners and smashes.
Speaking after the match, Kyrgios was asked about his on-court style and attitude.
And the world No 27 feels having different personalities on the tour will bring in new fans.
“I think it’s very important. You know, I think people are so concerned about keeping fans in the game, but I personally believe it’s about bringing in a whole new different fan base to the game,” he said.
“I think you look at the American sports like NBA, NFL, I mean, so exciting.
“I think they do it the right way, and I’m just trying to bring new fans to the sport. That’s one of my goals, actually, and I really want, you know, tennis to grow. I think there is so much potential for it to grow.
“I look at all the young players coming up, [Stefanos] Tsitsipas, Felix [Auger Aliassime], these guys, they all have different personalities.
“I think if the higher-up people in tennis market them the right way and we play the entertaining tennis we do, I think tennis can become pretty cool.”