She is 0-5 in that round previously. She will be replaced on Monday by Wimbledon champion Garbine Muguruza, who lost in the fourth round. Sloane Stephens, who had foot surgery in January and returned to the tour in July.
After two marathon five-setters to open his U.S. Open account, Federer sprinted past veteran Spaniard Feliciano Lopez in just 77 minutes in the third round and dismissed Kohlschreiber in one hour, 49 minutes without facing a break point.
He advanced to face 19-year-old Russian Andrey Rublev, the youngest quarterfinalist since Andy Roddick had just turned 19 in 2001.
Later on Monday, Federer ousted No. 33 seed Philipp Kohlschreiber 6-4, 6-2, 7-5 to reach the U.S. Open quarterfinals.
Federer did not face a break point and won in straight sets for the second time in a row after being pushed to five sets in each of the first two rounds. He will be Nadal's fifth straight unseeded opponent. This is the sixth time at the US Open that Nadal and Federer have each been one victory away from meeting.
The No 1 ranking is also at stake in today's matches.
Nadal is trying for his first U.S. Open quarterfinal appearance since winning the Grand Slam tournament in 2013.
Princess Mako's engagement celebrated but mood soured by N. Korea test
However, news of the engagement - and Mako giving up her royal status - didn't make headlines until earlier this year. Princess Mako's engagement is expected to be announced in the coming weeks, after which an official date will be set.
Nadal, also aiming for his third USA title after wins in 2010 and 2013, looked at his best after dropping the opening set of his first two matches.
She raced to a 4-0 lead and never let Brady get into the match in a much better performance than Saturday, when she struggled past No. 27 Zhang Shuai 3-6, 7-5, 6-4.
Vandeweghe echoed Williams' comments from after her quarterfinal victory, thinking back to the last generation of American women that, along with Venus and Serena Williams, included Lindsay Davenport and Jennifer Capriati.
While fans were still filing into Arthur Ashe Stadium, Nadal was wrapping up a clinical first set in 23 minutes.
Federer broke earlier in the second set to move ahead 3-2 and then gave himself additional breathing room with another break on the way to a straightforward 6-2 showing. The top-seeded Nadal faces Alexandr Dolgopolov on Monday afternoon.
Juan Martin del Potro prevented it once and can do it again.