Belgian top seed Henin and American number eight Williams have met in the past two grand-slam events, also at the quarter-final stage, with Henin winning at both the French Open and Wimbledon.
The world number one, who leads 6-5 in their career meetings, has romped through the first four rounds while Serena has struggled for top form.
"I'm going in feeling like I don't have anything to lose," said eighth seed Williams, who won her eighth grand slam title at the Australian Open in January.
"I just feel different now. Excited about the prospect of meeting her again."
French Open champion Henin, who won the title at Flushing Meadows in 2003, said she was looking forward to a match she knows is a spectacle for the fans.
"I know everyone was waiting for that match, and here we are," she said.
"That's why I'm playing tennis, to play this kind of match. I'm very happy I'm going play her, and I hope we can show good tennis. I think it's great for me."
Second seed Nadal, bidding for his first grand slam title outside of the French Open, plays compatriot David Ferrer for a place in the quarter-finals.
Nadal has been struggling with knee problems since the start of the event and will need to be at his best against Ferrer, who is in the fourth round for the first time, but who has won two titles this year.
Third seed Djokovic, looking to become the first Serbian man to win a grand slam, plays Argentine 23rd seed Juan Monaco.
Former world number one Carlos Moya meets Latvian teenager Ernests Gulbis, while 20th seed Juan Ignacio Chela of Argentina faces unseeded Swiss Stanislas Wawrinka.
