NEW YORK -- On the morning after she made history by winning her 308th career Grand Slam singles match, Serena Williams didn't sleep in at her hotel.

Instead, the soon-to-be 35-year-old was the first one on the practice courts at the USTA Billie Jean King National Tennis Center, preparing for a run toward her 23rd Grand Slam title.

Williams, the top seed, will meet No. 5 Simona Halep in the quarterfinals at 7 p.m. on Wednesday in Arthur Ashe Stadium.

"Serena Williams right now is playing for Grand Slam titles, she's playing to make history, she's playing to be No. 1," six-time US Open champion Chris Evert said Tuesday on ESPN.

As usual, Serena is the last American standing - man or woman -- after her sister Venus Williams was eliminated in three sets on Monday by Karolina Pliskova of the Czech Republic. Pliskova will meet Croatia's Ana Konjuh in Wednesday's daytime quarterfinal, with the winner to meet the Serena-Halep survivor in the semifinals on Thursday evening.

Serena appears to be on a collision course with No. 2 Angelique Kerber, which would be their third Grand Slam final of 2016. Kerber beat Serena to win the Australian Open in January, while Serena earned a measure of revenge in the Wimbledon final.

Kerber on Tuesday cruised past No. 7 Roberta Vinci, 7-5, 6-0, in the quarterfinals. Vinci, of course, stunned the tennis world with her Buster Douglas-like upset of Serena in last year's semifinals.

"It's always difficult to play against Roberta," said Kerber, who was down 4-5 in the opening set before winning the final nine games. "She's a great player and she played so well last year. I'm so happy to win it in two sets and to reach the semifinals again, it means a lot to me."

Serena must reach the final to have a chance of retaining her No. 1 world ranking. If Kerber makes the final, Williams will have to win the title to hold on to the top spot.

"That's a huge motivation [for Williams] because she thrives on these types of scenarios," Patrick McEnroe said on ESPN. "It's not a given that she's going to win these [matches]."

With every match win, Serena continues to make history.

Her 308th career Grand Slam win moved her past five-time Open champion Roger Federer (307), who did not enter the Open while resting his ailing knee. Martina Navratilova won 306 major matches en route to 18 career Grand Slam titles.

"I think it's really exciting," Serena said. "I just think winning 308 matches in general is pretty awesome. For that to be in a Grand Slam is pretty cool."

Nike recently dubbed Serena "the greatest female athlete ever" and then removed the qualifier in the ad, saying "Greatest. Athlete. Ever."

Asked is she could see herself playing another sport, Williams said, "Not really. I definitely want to stick to tennis right now. But, no, I never really thought about it."

As for Kerber, she is not allowing herself to think ahead to a potential third Grand Slam final meeting with Serena.

"I'm still trying to stay focused on match to match and when I came here I was telling myself to play round to round and going out to win my matches," Kerber said.

Kerber is playing in the shadow of one of the greatest of all time in fellow German Steffi Graf, who for the moment remains tied with Serena at 22 Open-Era titles.

"Of course, I mean Steffi is a champion," Kerber said. "When I was growing up I was always watching her playing. She's a great person. It's great to have her like an idol actually. It's tough to go in her steps. She won everything. It's also important to go in my own way."

That way could mean another epic meeting with Serena if both advance to Saturday's championship match.

Asked how important it was to envision herself winning the Open for a seventh time, Serena said:

"I think it's really important. You have to see it and believe it before it happens, you know. I think that is something that is super important."

Follow Adam Zagoria on Twitter @AdamZagoria for updates throughout the U.S. Open.