The Spaniard, who turns 20 on Friday, won the U.S. Open last September to become the youngest man to top the world rankings.

The 'Big Three' of Roger Federer, Rafael Nadal and Novak Djokovic have dominated men's tennis for nearly 20 years, collectively winning 64 Grand Slams.

While only Djokovic and Nadal still active, Alcaraz said reaching their level will be a daunting task.

"Well, my dream in tennis right now is to become one of the best players in history," Alcaraz told reporters after beating Karen Khachanov 6-4 7-5 in the Madrid Open quarter-finals on Wednesday.

"In this world, you have to dream big and you have to think big, as well," Alcaraz said. "I want to be part of the best tennis players in history and I'll work for it."

Alcaraz, who is seeking a fourth title of the season after triumphs in Buenos Aires, Indian Wells and Barcelona, continues his Madrid title defence on Friday when he takes on Croatian Borna Coric in the semi-finals.

Alcaraz said he plans to play in Rome next week as he builds up for the French Open, which starts on May 28th.