With 20th birthday looming, Carlos Alcaraz underscores his big ambitions

WATCH: Alcaraz ran his winning streak in Madrid to nine matches after with his quarterfinal victory over Khachanov.

As he readies to enter his next decade of life, Carlos Alcaraz is doubling down on his lofty tennis ambitions.

Alcaraz's place in tennis history is already assured, as the youngest-ever man to reach world No. 1 and the youngest US Open champion in more than 30 years with his 2021 triumph. But after beating Karen Khachanov in the quarterfinals of the Mutua Madrid Open, the Spaniard, who turns 20 on Friday, says he will always want more.

"My dream on tennis right now is to become one of the best tennis players in history. I know that this is a big dream, probably is too big," he said Wednesday, with a now-famous grin. "But in this world, you have to dream big and you have to think big, as well.

"I want to be part of the best tennis players in history and I will work for it."

Earlier in the week, Alcaraz expounded on the life-changing 12 months he's experienced since he last walked the grounds of the Caja Mágica, and how he's managed to stay grounded despite it all. Last year, days after turning 19, he became the youngest champion in tournament history and became the first player to ever beat both Novak Djokovic and Rafael Nadal at the same clay-court tournament.

"It feels different comparing for last year. I'm not the young player that is coming up. I'm there," he said. "More attention, more and more people coming to my match, to my practice. ... It feels different, but at the same time, it feels a bit great.

I'm a normal guy. I think that I'm not really, really famous. I will always be the same person with my people, my parents. I think my parents did a great job when I was really young. Nothing happens to me. I always be the same. Nothing changes for me."

Whether or not Alcaraz views himself as a celebrity, the star-studded support system he's had at home might disagree: This week, famed Grand Prix motorcycle road racer Marc Marquez, and several stars of the Real Madrid soccer team, have been among those spotted in the stands cheering him on.

Currently on a nine-match winning streak after triumphing in Barcelona for his third title of the season, Alcaraz is bidding to make recent history in Madrid: He hopes to be the first man to win back-to-back titles at the Caja Magica since Rafael Nadal in 2013-14.

In his first match as a 20-year-old, Alcaraz face No. 17 seed Borna Coric in Friday's semifinals.