NEW YORK — Serena Williams could play an All-American U.S. Open.

As she seeks the first Grand Slam since 1988, the top-ranked Williams might find herself competing against the past and future of her country’s championship hopes.

A potential third-round opponent is 22-year-old Sloane Stephens, who beat her in the 2013 Australian Open quarterfinals and is coming off her first WTA title in Washington this month. A possible fourth-round foe is 20-year-old Madison Keys, who reached this year’s Aussie semifinals.

Then in the quarterfinals, she could face her sister, seven-time Grand Slam winner Venus Williams. Serena had to beat Venus in the fourth round at Wimbledon on the way to her second “Serena Slam” — four major championships in a row, but just not in the same year.

Now Williams is attempting to complete the first Grand Slam since Steffi Graf 27 years ago.

Asked about the potential matchup with her sister after Thursday’s draw ceremony, Williams laughed and said: “It’s better than the round of 16, so that’s how I look at it.”

Another potential quarterfinal opponent is 12th-seeded Swiss teen Belinda Bencic, who recently upset Williams in Toronto en route to a breakthrough title. Williams could face Maria Sharapova for the second straight major semifinal after beating her for the 17th consecutive time at Wimbledon.

There are nine U.S. players in all in Williams’ quarter of the bracket. Based on recent results, facing the young Americans early in the tournament could help keep Williams sharp under the pressure of her Grand Slam pursuit.

Since the upset by Stephens in early 2013, Williams has lost just once to a countrywoman — to Venus more than a year ago. Of course, she hasn’t lost much to anyone during that span.