Title favourites Roger Federer and Rafael Nadal will begin their US Open campaigns in New York on Tuesday.
The pair have never met at Flushing Meadows but could face each other in the semi-finals this year.
"I'd be happy to play him here - I don't think we are thinking that far ahead," said Federer.
Women's world number one Karolina Pliskova, defending champion Angelique Kerber and Britain's Aljaz Bedene are also in action on day two.
Czech Pliskova opens play on Arthur Ashe Stadium at 16:00 BST against Poland's Magda Linette, followed by Germany's Kerber against Naomi Osaka of Japan.