The 19-year-old Spaniard can become the youngest Grand Slam men's finalist and champion since Nadal won his first major at the 2005 French Open.
As well as being tantalisingly within touching distance of a maiden Slam of his own, Alcaraz could also be crowned the youngest men's world number one of all time should he make the final.
"As long as Rafa, Djokovic, Federer are there, they will be the best and the rivalry they have between them will always come first," said Alcaraz after seeing off 21-year-old Jannik Sinner in his five-hour 15-minute quarter-final.
"But Jannik and I have shown that we are the present and we also have long careers ahead of us."
Alcaraz tackles Frances Tiafoe, who knocked out Nadal in the fourth round, in his semi-final with the winner to face either Karen Khachanov or Casper Ruud.
The four men have a combined age of 94 - the youngest at a Slam since New York in 2008 when Federer, Nadal, Djokovic and Andy Murray made the last four.
Djokovic, a three-time champion in New York, didn't play the tournament this year after being banned from entering the US over his refusal to be vaccinated.
Federer, a six-time winner, has been sidelined for over a year with a knee injury.
Despite history beckoning for Alcaraz, he has had to endure a rollercoaster ride through to his maiden appearance in the semi-finals of a major.
After sailing through the first three rounds, he needed five sets to defeat 2014 champion Marin Cilic in a last-16 tie which ended at 02:23 a.m. on Tuesday.
His quarter-final against Sinner, another five-setter, began on Wednesday and ended at 2:50 a.m. Thursday.
It was the second-longest US Open match ever and surpassed the previous record for latest finish of 2:26 a.m. On the way, Alcaraz saved a match point.
He spent more than nine hours on court in those two matches and a shade over 16 hours in total over his five rounds.
'Bit surprised'
Tiafoe, meanwhile, has also made the semi-finals of a Slam for the first time.
The 24-year-old is on course to become the first Black male player to win the US Open since Arthur Ashe in 1968.
Tiafoe's rags-to-riches back story has captivated the tournament.
The son of immigrants from Sierra Leone, his father worked as a caretaker at a tennis club in Maryland where Tiafoe learned the game.
"Every time I win, I just want to inspire a bunch of people to just know that anything is possible," Tiafoe said.
The charismatic American spent three hours fewer than Alcaraz getting through his last two rounds.
He also defeated Alcaraz in their lone previous meeting, winning on the Barcelona clay in straight sets last year.
Norwegian world number seven Ruud, who also has a chance to take the world number one ranking, is into his second semi-final at the Slams after going all the way to a runner-up finish at the French Open in June.
The 23-year-old made the last four with a surprisingly easy straight-sets quarter-final win over Matteo Berrettini, a semi-finalist in 2019.
"I'm honestly a bit surprised that I made it to the semis," admitted Ruud whose three titles in 2022 have all come on clay.
However, he gave a glimpse of his hard court prowess by making the final in Miami earlier this year.
"I think I have developed my hard court game a lot the last year or two, and I think in Miami I proved to myself that I can beat good players and reach the later stages."
Khachanov lost his only previous meeting with Ruud on clay in Rome in 2020.
However, he made the semi-finals with a five-set win over Nick Kyrgios who had knocked defending champion and world number one Daniil Medvedev out of the tournament.
The 26-year-old Russian has sent down 88 aces at the tournament, second only to Kyrgios.
"It's like one more step forward," said Khachanov of making the semi-finals having never previously got beyond the third round in six previous visits.
