The world number one will face the 21-year-old for the first time at Roland Garros after Khachanov overcame John Isner to advance into the last 16 of a Grand Slam for the first time in his career.
Murray has struggled on clay at times this year, but he is confident that he is beginning to find his form again following some improved showings so far at the French Open.
"I have never played a match against him, but I practised with him before he got on to the tour when he was like 350 (in the rankings), and he was really good. Big, strong guy. Generates a lot of power. He's also got a big serve," he told reporters.
"I believe in myself, so even when things aren't going well, I believe I can turn it around. It's not easy but, if you do the right things in practice and trust it, it's going to come.
"The five-set format has definitely helped, so I have maybe not been as anxious going into some of the matches, because I know there is some time to turn it around. But mentally I feel pretty good just now. I'm working things out while I'm playing the matches, and that's a really, really important part of my game."
Murray is bidding to reach the final of the French Open for the second year in a row.