Williams and Sharapova will face each other for the first time in the last 16 since the quarter-final of the 2016 Australian Open, which was Sharapova's last match before a 15-month doping ban.
"This is the first time I've come into an event with, really, not too many expectations, you know".
"I'm just really trying to get my bearings and trying to feel out where I am and see where I can go".
After the deluge of words that accompanied the most anticipated collision of this French Open there is a gathering conviction here that Maria Sharapova will emerge from her fourth-round match on Monday celebrating her first win over Serena Williams in 19 matches, leavened only by the obligatory nod of consolation. It was the first time Sharapova showed a killer instinct and didn't have so many hiccups with her second serve. "We are both on a comeback - for two totally different reasons - and she's been on her journey for over a year and I just started mine a couple months ago".
Williams and Sharapova are slated to play at 8:15 a.m. ET on Monday morning.
Sharapova's autobiography, published past year, contained several passages about Williams.
"She's probably a favourite in this match", said Williams.
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"I was one of the few people that said that she was courageous to say something", said Williams referring to Sharapova's "drug incident".
"But, of course, I came into Europe and Stuttgart with not a great record, not playing great tennis with a lot of injuries, and have been able to turn that around a little bit".
The pair's fierce rivalry has been dominated ever since by Williams, who has won the past 18 matches against Sharapova.
Other women moving into the fourth round included 2016 champion Garbine Muguruza, two-time French Open finalist Simona Halep, two-time major title victor Angelique Kerber and reigning U.S. Open champion Sloane Stephens.
Earlier on Saturday, Russian two-time victor Sharapova beat sixth seed Karolina Pliskova 6-2 6-1.
Either way, the verdict here says Williams won this tournament just by being out there.
The 38th-ranked Khachanov has made it to the fourth round both times he played at Roland Garros, his best showing at any Grand Slam tournament.
The way in which Sharapova sent down winners down the line and displayed powerful shots to win her points evoked memories of her early days as a player and sent out a clear message that she was here for the long haul and could possibly end up winning the title.
Indeed, if she fulfils the majority of predictions here - having looked devastatingly good thrashing the world No 6 Karolina Pliskova in the third round - and actually beats Williams, it is hard to imagine she will be able to contain that ice-cool facade for long. "I managed to stay aggressive and I played smart as well", said Sharapova, who delighted a half-full stadium by thanking them for their support in French.