"Now I just have to go find her, because I need to tell her some juicy stuff", the 25-year-old said after setting up a repeat of last year's U.S. Open final showdown.
There were no gifts from Keys on court, however, as she came from 5-3 down in the opening set to see off her unseeded opponent.
Keys had earlier beaten Yulia Putintseva and when Stephens showed patience before overpowering Kasatkina it ensured that two Americans would face each other in the French Open semi-finals for the first time since 2002 when Serena Williams defeated Jennifer Capriati.
After beating No. 31 Mihaela Buzarnescu of Romania 6-1, 6-4, she next faces either No. 26 Barbora Strycova of the Czech Republic or Yulia Putintseva of Kazakhstan.
At this year's French Open, where notable upsets of Ostapenko, Venus Williams and Petra Kvitova have grabbed the headlines, Sloane Stephens has carried a sense of optimism back on the court. But like Stephens, Kasatkina found herself severely tested in the third round, where she took on Maria Sakkari in a seesawing match.
At 21, Zverev is the youngest quarterfinalist at Roland Garros since Juan Martin del Potro in 2009. "I think there's a difference between being intense and wanting it and fighting and just not being nice, so that's something that I have always stayed true to". With Keys by now making a flurry of unforced errors, the US Open champion was able to close in on victory as she held for a 3-1 lead just like in the first set.
Halep, who lost in last year's final, broke the 16th-seeded Belgian's serve six times on Court Philippe Chatrier. Impressively, she has yet to drop a set here, and makes her first non-hardcourt semi-final berth. Her start to the 2018 season was blighted by inconsistency and poor form which resulted in first round defeats in Sydney and Melbourne.
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She clinched the victory on her first match point with a forehand victor from the baseline.
The quarterfinals on the other side of the draw are Wednesday, involving four women who have spent time at No. 1: Simona Halep, who now leads the WTA rankings, against No. 12 seed Angelique Kerber, and No. 3 Garbine Muguruza against No. 28 Maria Sharapova.
"It's always a special moment to qualify in the final of a Grand Slam".
Halep will play Madison Keys or Sloane Stephens in Saturday's final.
Madison Keys is thinking big at the French Open after reaching the quarterfinals for the first time. "And the right tactic was that I didn't miss anymore."- Halep, commenting on her strategies.
Stephens, who had never gone past the fourth round in Paris, will take on twice French Open runner-up and world number one Simona Halep of Romania in Saturday's final.
Now comes challenge of taking on Nadal at Roland Garros.