She beat Aryna Sabalenka in the final in September to claim her first major title.
Last week the 19-year-old American defended her Auckland Classic title in preparation for the Australian Open, which begins on Sunday. Asked if she had a number of Grand Slams in mind, Gauff said it would be “cool” to get to “double digits”.
“I don’t know if it will happen, but that’s a high goal,” she said.
“Setting my goals high pushes me beyond what I think I can do.”
Only seven women have won 10 or more Grand Slam singles titles.
Margaret Court holds the record with 24, while Venus Williams’ tally of seven is the highest among current players. World number four Gauff, who has won 29 of her past 33 matches, is among the favourites to win the Australian Open.
“During the off-season we did celebrate a little bit just because after the US Open everything was so fast,” said Gauff, who faces Slovakia’s Anna Karolina Schmiedlova in the first round in Melbourne on Monday.
“It really feels like so long ago. Some players’ goal is to win a Grand Slam. Once they reach that, it’s kind of ‘what’s next?’ “I always knew I wanted to win multiple.
“The only thing I will try to remember from [the US Open] is just the way that I won. It wasn’t my best tennis. It was more the mental fire.”
In the US Open final Gauff lost the opening set to defending Australian Open champion Sabalenka before fighting back to win 2-6 6-3 6-2.
