"I have no expectations, no pressure", said Halep after seeing off German 12th seed Angelique Kerber 6-7 (2/7), 6-3, 6-2 in the quarter-finals on Wednesday.
Garbine Muguruza's big strokes overwhelmed Maria Sharapova right from the start.
"That means one American will be in the final of a French Open, which is another fantastic thing", Stephens said.
"I just have to go find her, because I need to tell her some juicy stuff", Stephens said, declining to reveal the topic.
Former number one Muguruza takes on current incumbent Halep on Thursday with the victor to be assured of the top ranking as well as a place in the Roland Garros final.
"But on the day I can leave a Grand Slam saying I gave everything I had, I played a great match, is not here yet".
Nadal, a 10-time champion at Roland Garros, had not ceded a set in Paris since 2015, when he was beaten in the quarterfinals by Novak Djokovic.
Nadal lost the opener 6-4 against 11th-seeded Diego Schwartzman but began to play better after a rain delay of just under an hour.
In the other men's quarterfinal, No 3 Marin Cilic and No 5 Juan Martin del Potro were at 5-5 in a first-set tiebreaker when the matchup of past US Open champions was stopped.
By the end of the first set, the 5-time major victor had won just 8 points against the Muguruza serve and failed to carve out a single break point. She is capable of moving Muguruza and forcing her out of her comfort zone in a way Sharapova could not.
She is one of two semi-finalists - alongside Garbine Muguruza - who are yet to drop a set this fortnight in Paris.
Sharapova certainly didn't do that.
Halep has only dropped one set en route to the last eight, back at the start of the tournament when she lost the opening set of her first-round clash with American Alison Riske.
It took her 29 minutes just to gain a game, and by then she already trailed 4-0. "I missed a lot at the beginning of the match".
Sharapova didn't play a point in the fourth round, because Serena Williams pulled out of their much-anticipated showdown with an injured chest muscle.
Muguruza's opponent Lesia Tsurenko lasted just two games before retiring hurt.
"Kind of a weird day", Muguruza said.
Just like she wowed the tennis world with her summer previous year, Stephens is enjoying a strong spring that started with her winning the title in Miami. Muguruza, who won the French Open in 2016 but didn't make it out of sectionals past year, is continuing a fantastic run of tennis at Roland-Garros.
Halep, meanwhile, has participated in a trio of major finals, losing each. Halep's only win over Muguruza came in the 2016 Stuttgart Open, the only meeting between these two on clay.
It ranked among one of the most lopsided losses ever suffered by Sharapova in her Grand Slam career.
Halep broke Kerber in the very first game and then managed a strong hold to go 2-0 up.
Keys built a whopping 30-12 edge in winners and won 84 percent of her first-serve points.
But Halep figured things out.
But this gesture towards her coach Darren Cahill was more than a celebratory pose, it was a sign that this was 'the new Simo'.
And sure enough, we have seen a more tenacious Halep at play over the a year ago, despite the glaring hole of two Grand Slam runner-up trophies in the space of eight months.