Alcaraz beat chief rival Jannik Sinner 6-2, 3-6, 6-1, 6-4 to claim his second US Open crown and would become the youngest man to win all four majors if he lifts the trophy in Melbourne next January.
"It's my first goal, to be honest," said the 22-year-old Alcaraz, who has not made it past the quarter-finals in four trips to Australia.
"When I just go to the preseasons to what I want to improve, what I want to achieve, Australian Open is there.
"It's the first or second tournament of the year, and it is always the main goal for me to complete a career Grand Slam, calendar Grand Slam. So it's going to be great."
Alcaraz's compatriot Rafael Nadal holds the record as the youngest man to win all four majors. He achieved the feat at the age of 24 in 2010 when he won the first of his four US Open titles.
"Obviously I'm going to try to do it next year, but if it is not next year, hopefully in two and three and four. So I will try to complete it," said Alcaraz.
He will reclaim the world number one ranking from Sinner on Monday, returning to the top of the men's game for the first time since September 2023.
"When you achieve the goals you set up yourself at the beginning of the year, it feels amazing," said Alcaraz.
"Since I got the chance to recover the number one, it was one of the first goals that I had during the seasons, just to try to recover the number one as soon as possible or end the year as the number one.
"For me, to achieve that once again, it is, as I said, it is a dream. Doing it the same day as getting another Grand Slam feels even better."
Alcaraz dropped just one set throughout the tournament and continued his recent mastery of Sinner, getting revenge for his loss to the Italian in the Wimbledon final.
"The performance today was perfect," said Alcaraz's coach Juan Carlos Ferrero.
Alcaraz and Sinner are the torch-bearers of the current generation, sweeping the last eight majors between them and taking 10 of the last 13. Novak Djokovic has won the other three.
Ferrero knows Alcaraz has the talent to hoover up considerably more silverware in the years to come but is doing his best to ensure his protégé keeps working hard at his craft.
"The potential to win many titles, many Grand Slams, is there, but we take nothing for granted. Nothing is automatic; you have to make it happen," said Ferrero.
"I don't think too far ahead. I can't stop to think about whether Carlos is going to win 20 Grand Slams; you have to take each day as it comes.
"He's 22 years old; we can't think he's perfect, far from it. He has a lot of things to improve on."