Novak Djokovic warns his Grand Slam quest faces a tough challenge from Italian sixth seed Marco Berrettini in the US Open quarter-finals as they meet in a third consecutive Slam.

The 34-year-old Serbian advanced within three matches of completing the first calendar-year Grand Slam in 52 years on Monday by fending off 99th-ranked American Jenson Brooksby 1-6, 6-3, 6-2, 6-2.

Not since Rod Laver in 1969 has a man swept all four major titles in the same year.

If top-ranked Djokovic wins his fourth career US Open crown, he will have a men's all-time record 21 Slam titles, breaking the deadlock he now has with Roger Federer and Rafael Nadal, both absent with injuries.

Next up for the world number one is a Wimbledon final rematch against Berrettini, whom Djokovic called the "Hammer of Tennis" as "probably the hardest hitter of serve and forehand" next to 2009 US Open winner Juan Martin del Potro.

"He's got the lethal-serve-plus-one game. He's already established as a top player," Djokovic said. "If he serves well, which is his biggest weapon, he's tough. He's tough on any surface to play against."

Djokovic beat Berrettini in four sets in both a French Open quarter-final and July's Wimbledon final, and won their only other meeting at the 2019 ATP Finals. He hopes to put the Hammer down once more.

"We're going to play the third Grand Slam in a row against each other," he said. "Hopefully the result will be the same like the previous two."

Djokovic had a tussle with Brooksby until fitness factored in and the 20-year-old wildcard could not move around the court.

"Expected the battle, and I got one," Djokovic said. "I'm pleased to overcome it."

A tweet by 2003 US Open winner Andy Roddick during the match noted of Djokovic, "First he takes your legs... Then he takes your soul."

"Thanks Andy," Djokovic said. "I'll take that as a compliment, the first part.

"The second part, I don't take anybody's souls... But I'll take your legs out, that's for sure."

Djokovic was delighted to play before a full crowd at Arthur Ashe Stadium in the wake of limited crowds at prior Slams due to the Covid-19 pandemic.

"People missed the action, missed the entertainment, being locked up for more than a year," he said. "Now under certain conditions you are able to go and watch sports live, which is nice.

"Last year and a half was tough for everyone, so it's really refreshing and it's really beautiful to see a full stadium."

'What a great ride'

As his potential date with history moved nearer, Djokovic recalled dyeing his hair for his first Slam match as a 17-year-old at the 2005 Australian Open.

"It wasn't really very satisfying for my mother to see that," Djokovic recalled. "The conversation we had after was not great for me. But we had a good laugh about it.

"That seems like ages ago, and it is. I mean, it has been now 16 years since my first center court Grand Slam match. It has been a while.

"But what a great ride."

Djokovic said it wasn't easy to look back while he's still trying to write history.

"It's difficult to reflect on everything while you're still in the bus and you're still riding," said Djokovic. "It's kind of hard. People tend to ask me, 'How does it feel? Do you comprehend what you've done? Do you think about the whole journey?'

"Of course, I do. But tennis is such a sport that really you have to turn the next page the next day.

"You don't have much time, really, and energy to reflect on everything that you've been through. But I try to be grateful about it. Of course, I appreciate every single step in the journey."