In the women's draw, Serena Williams, bidding for a seventh US Open title and an Open era record 23rd Grand Slam, begins her campaign against experienced Ekaterina Makarova of Russian Federation. But he got some much-needed rest after arriving in NY on Sunday, taking both Monday and Tuesday off.
Meanwhile, World number one Djokovic admitted that he's not 100 percent fit as he prepares to defend his title.
Williams then lost in January's Australian Open final to Germany's Angelique Kerber - who will be guaranteed the No. 1 ranking if she wins the title on September 10 - while Spain's Garbine Muguruza outplayed her in the final at Roland Garros.
The season has already produced momentous achievements, with Williams matching Steffi Graf for most slams in the Open era with her 22nd, won at Wimbledon over Kerber.
Federer, 35, Nadal, 30, Djokovic and Murray, both 29, have together won 45 of the last 51 grand slams but Murray admits there is now a chink of light for the rest of the field.
After becoming the first player to defend an Olympic singles title, Murray - who faces Lukas Rosol of the Czech Republic on Tuesday - is chasing more history in NY.
"I think today I can start the forehand, I think my normal forehand, but it still needs time to feel that I am more confident on my wrist".
Makarova made two straight major semis at the 2014 U.S. Open, losing to Williams, and the 2015 Australian Open. The Serb champion has great memories at Flushing Meadows. At the Rio Olympics, Keys played for the bronze medal.
In the other quarter in Serena's side of the draw, the leading seeds are Agnieszka Radwanska of Poland (4) and Venus Williams (6), who will aim for a semi-finals encounter with her sister.
Nadal is a potential semifinal opponent for Djokovic, the defending champ, while Andy Murray and Stan Wawrinka are in the other half of the bracket. But the 19th-seeded Johnson could face the Olympic silver medalist in the second round. Having struggled with injuries in the past, she now also travels with renowned fitness trainer Scott Byrnes.
So Friday's draw could create a daunting opening match for a seeded player.
As for the No 1 spot, Murray knows that being consistent week in, week out, is the only way to topple Djokovic, who looked so unstoppable before his third-round defeat at Wimbledon and first-round loss in Rio.
Williams must contend with Germany's Angelique Kerber, the Australian Open victor who would have become world number one had she not lost the final at last week's Western & Southern Open in Cincinnati.
In 2009, Juan Martin del Potro became the first man to defeat Nadal and Roger Federer in the same Grand Slam tournament to capture the US Open in a powerfully emotional performance that earned him a devoted fan following in NY.
Serena Williams once again arrives at Flushing Meadows poised to rewrite the tennis record books - if her own troublesome right shoulder and increasingly emboldened rivals allow.
Puig beat three Grand Slam champions in Rio de Janeiro in her surprise run to gold, while del Potro has defeated three of the U.S. Open's top four seeds since the start of Wimbledon.