NEW YORK — With each round of the U.S. Open, it looks increasingly likely that Novak Djokovic will make history Sunday at Arthur Ashe Stadium.

The world’s No. 1 player needs to win only four more matches to claim his 21st major, breaking his tie with Roger Federer and Rafael Nadal for the most in men’s history, and become the first man since Rod Laver in 1969 to complete a calendar-year Grand Slam.

While his success remains to be seen, what is certain is that each time Djokovic steps on court between now and then, he will be booed by at least some segment of fans at Arthur Ashe Stadium.

Djokovic is so cognizant of this, after 15 previous U.S. Opens, that he heard boos when none were audible — mistaking howls of “Roooooon!” that in fact were cheers for his first-round challenger, 18-year-old Holger Rune of Denmark.

“It was not ideal atmosphere for me, to tell you that,” Djokovic, a three-time U.S. Open champion, said after hearing what sounded like boos. “But I’ve been in these particular atmospheres before, so I knew how to handle it.”

If he sustains his peerless trajectory of late, Djokovic probably will retire as the greatest man to play the game. It is a status his ardent followers are prepared to confer today, given his superior head-to-head record over both Federer (27-23) and Nadal (30-28).

But it is a status others will confer grudgingly, if ever.

There are those who dislike the Serb for particular reasons. Among oft-cited grievances are questionably timed medical timeouts earlier in his career and breaks that smack of gamesmanship. And then there are infrequent yet dramatic on-court eruptions, such as the angry blast of the tennis ball that unintentionally struck a 2020 U.S. Open linesperson and resulted in his disqualification or the racket-throwing episode at the 2021 Tokyo Olympics, where his pursuit of the rare Golden Slam ended with a semifinal defeat.

Others dislike Djokovic simply because they love Federer or Nadal more, so they actively root against his bid to surpass their idols’ shared mark of 20 majors.

But what more can Djokovic do to win over his detractors?

If the point of sport is excellence, Djokovic needs to do nothing more than continue the dominance he has displayed all season. He has been on a torrid run, 24-0 in Grand Slam matches since the Australian Open got underway. With his ninth title in Melbourne, Djokovic pulled within two of Federer and Nadal. He vanquished Nadal on the red clay of Roland Garros, which is a career-defining achievement in itself, en route to the French Open championship, which brought him to 19. And he drew even at Wimbledon.

At 34, Djokovic stands on the precipice of tennis history not simply because he has outlasted 40-year-old Federer and 35-year-old Nadal, who both shut down their 2021 campaigns to address lingering injuries.

He has painstakingly crafted a plan — and assiduously followed it — to forge himself into the world’s greatest tennis player. Helped by a large, loyal team that includes coaches Marian Vajda and 2001 Wimbledon champion Goran Ivanisevic, as well as a fitness coach and counsel from a dietitian and mental coach, Djokovic embarked years ago on a mission of continual improvement, to borrow a business term, designed to transform a once wiry also-ran in the Federer-Nadal battle for tennis hegemony into a purpose-built winning machine.

“He always had lots of qualities on the court, had a very solid all-around game,” recalled three-time Grand Slam champion Andy Murray, who has competed against Djokovic since both were juniors. “But … I don’t think many people would have predicted that he would go on to win 20 Grand Slams, trying to do what he’s going to do here.”

Murray attributes the transformation to hard work.

“If you look at his game over the years, the things he’s improved — he has turned himself into a complete player,” Murray said. “He plays great on all surfaces. He has an underrated serve. He’s the best returner of all time.”

Djokovic’s climb up the rankings has included the adoption of a gluten-free diet and a disciplined yoga practice with a focus on flexibility, which has helped him avoid injury while earning nicknames such as “Spider-Man” and “Gumby” for his often-contortionist defensive prowess.

Though his serve was never a liability, he has improved that, too, with help from Ivanisevic, focusing on placement over power.

His mental game is fierce. That, too, is the product of hard work, acquired and steeled through meditation, conscious breathing, visualization and other disciplines.

While all top-ranked players push themselves, Djokovic, by all accounts, simply has been more intense about it — particularly when Grand Slam titles are at stake.

He also hasn’t hesitated to proclaim his goals out loud — including the calendar-year Grand Slam.

Whether that’s a declaration of well-deserved pride or hubris that may bite him in the end is uncertain.

Laver, now 83, raised the possibility of the latter, albeit in diplomatic fashion, in an interview with the Associated Press this summer.

“I never said I was going for a Grand Slam; that’s pressure right there,” said Laver, the only player to have twice claimed a calendar-year Grand Slam, in 1962, when tennis was contested by amateurs, and again in 1969. “And Djokovic, I think he wants to talk about it, and so that could be a detriment, if there is one.”

So far, there’s no sign Djokovic’s stated ambition is doing anything but working in his favor.

His year-to-date record is 41-5. And his comeback against Stefanos Tsitsipas in the final of the French Open, in which he clawed back from a two-sets-to-none deficit, was a testament to his physical and mental resolve.

“I thrive under pressure,” Djokovic said on the eve of the U.S. Open, brushing off a suggestion that all the expectation surrounding his Grand Slam bid may prove his biggest opponent. “This is what you work for day in, day out, all your life, to put yourself in a unique position to win Grand Slams and to make history. At the end of the day, I’m a big tennis fan, fan of history. I admire this sport. I love it. I have this chance, and I’m going to try to use it.”