Chung was the biggest surprise package at the Australian Open last month as he battled his way to the semi-finals of a Grand Slam for the first time.
The 21-year-old knocked out former world number one Novak Djokovic on his way to the last four.
But a clash with Roger Federer proved too much for Chung and he retired towards the end of the second set through injury.
Chung will be fondly remembered for his epic rise to fame during the tournament and now he claims he wants to go one better by winning a major competition.
Federer and Nadal are expected to sweep up all four titles between them again this season, as they did in 2017.
But Chung has ambitions to break that mould, beginning with the French Open which starts in May.
“I’ve not set any specific target (for the French Open) but I will be able to win a Grand Slam tournament some day in the future,” Chung said.
“My performance on clay courts was good last year.”
After his defeat to Federer, Chung posted a picture of his badly blistered foot on Instagram.
And he received a lot of support from fans who labelled him “brave “ and “courageous”.
“I’ve seldom played so many games unremittingly and my feet reached their limits,” Chung said.
“My doctor says the blistered feet are curing well due to my young age and I will be able to start training next week.”