Sloane Stephens faces Madison Keys in a repeat of the 2017 US Open final in an all-American line-up in the other semi-final. Muguruza hopes to make her fourth career grand slam final and her second career French Open final. Last year, he took the trophy without dropping a set.
That semi-final will also decide the number one spot next week.
"It's the same thing as always". Stephens chimed in to reporters: "We are not going to be weird and awkward and make it, like, weird for each other".
"I just have to go find her, because I need to tell her some juicy stuff", Stephens said, declining to reveal the topic.
On whether Williams's late withdrawal in the previous round had derailed her momentum in the tournament she said: 'I didn't really know what to do.
"I think it would be odd for me not to include someone that I have competed against for so many years", said the 31-year-old. "And also physical, for sure, but mentally I was strong". I'm playing well, in a good space.
Both were appearing in the quarterfinals on the red clay of Paris for the first time, and both handled the occasion well. Off the baseline, Stephens will bait Keys to go for too much, using her speed and counter-punching ability to shrink the court. When you're writing an autobiography, I don't think there is any reason to write anything that's not true'. Some of those matches were very defining for me. "She served a lot better than I did". "I'm not ever going to try to be a person that isn't nice, so that feels more authentic to me and I think I'm still doing okay while trying to be as nice as possible".
However, the match looked increasingly lopsided to start with as Kerber sent down some stunning winners while Halep fudged simple shots and found the net more often than winners. However, if you're picking this match based on the current form, you can't pick against Muguruza. As she told the press after her quarterfinal win, "There were times when I had to go back and hit a higher ball, where maybe before I would have tried to hit a line-drive victor".
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But this gesture towards her coach Darren Cahill was more than a celebratory pose, it was a sign that this was 'the new Simo'. Keys is all-out attack.
The women got their matches done before rain arrived at Roland Garros, leaving the men's quarterfinals suspended in progress. Muguruza, the 2016 French Open champion, was world number one for four weeks from September 11 to October 8 a year ago. Stephens has made the second week in Paris in five of her seven appearances and Keys is slowly coming to terms with the surface.
Halep is still chasing her first Grand Slam title after several near-misses.
Stephens has won both head-to-head encounters, including the Grand Slam final debut for each at NY in September.
The signs were ominous when the five-times Grand Slam champion coughed up three nervy double-faults in the opening game.
And she admitted that even in her quarter-final clash with Kerber on Wednesday, it was her mental game that finally gave her the edge.
A win on Thursday would move Stephens to No. 4 in the rankings.