The Spaniard will play either 24-time Grand Slam champion Novak Djokovic or last year's runner-up Taylor Fritz on Friday for a place in the final.
Alcaraz is yet to lose a set at the tournament in his quest for a sixth Grand Slam title. He won his first major at the US Open in 2022 as a teenager.
The 22-year-old can reclaim the world number one ranking from Jannik Sinner with another triumph in New York.
"It's really difficult not to think about it," said Alcaraz.
"Every time I step onto the court I try not to think about it. If I think about the number one spot too much I think I'm going to put pressure on myself and I don't want to do that."
Alcaraz, who again celebrated his win with an imaginary golf swing, said he would squeeze in another round on the course -- with former Masters champion Sergio Garcia -- in the two days off before his semi-final.
"It's something that's working well so why should I change that routine," said Alcaraz. "Every day off I go and try to play some golf."