NEW YORK >> Serena and Venus Williams could be headed toward their earliest Grand Slam meeting in 20 years, facing a potential third-round matchup at the U.S. Open.

If the sisters do play each other, the winner might face No. 1-ranked Simona Halep in the fourth round.

That section of the women’s bracket, and a possible Roger Federer-Novak Djokovic quarterfinal showdown in the men’s, provided the most intrigue when the brackets were revealed at Thursday’s draw for the last major of the year.

This marks Serena’s return to Flushing Meadows after missing the hard-court tournament in 2017 — she gave birth to her daughter last Sept. 1.

The 36-year-old American has won six of her 23 Grand Slam titles at the U.S. Open and was given the No. 17 seed by the U.S. Tennis Association — nine places above her current ranking.

Venus, who won five of her seven Grand Slam singles trophies in New York, is ranked and seeded 16th. She faces a tricky first-round match against Svetlana Kuznetsova, whose two major championships include the 2004 U.S. Open.

Kuznetsova was given a wild-card entry for the tournament, where main-draw play begins Monday.

Serena’s opener comes against 60th-ranked Magda Linette of Poland. Should the Williams siblings both make it to the third round, they would play each other at a Grand Slam tournament sooner than they have since Venus beat Serena in the second round at the 1998 Australian Open — their very first head-to-head match on tour.

They’ve gone on to play a total of 29 times — Serena leads 17-12 — and that includes nine all-in-the-family Grand Slam finals, most recently at the 2017 Australian Open.

In the men’s field, No. 1-ranked and defending champion Rafael Nadal opens against David Ferrer in an all-Spanish rematch of their 2013 French Open final. No. 2 Federer plays Japan’s Yoshihito Nishioka in the first round.

Federer lost in the quarterfinals last year and this time in that round could face No. 6 seed Djokovic, the Wimbledon champion who beat him two weeks ago in a tuneup and is considered a tournament favorite after having to miss it last year because of injury.

Nadal, however, isn’t sure there is one.

“Of course Novak and Roger, they are doing very well and especially they like the hard courts,” he said during the draw ceremony by the Hudson River in Lower Manhattan. “Let’s see. Let’s see what’s going on.”

No. 4 seed Alexander Zverev and seventh-seeded Marin Cilic, the 2014 U.S. Open champion, are also in Federer’s half of the draw along with No. 30 seed Nick Kyrgios, the Australian whom Federer could meet in the third round.

Stan Wawrinka, the 2016 U.S. Open champion who missed last year’s tournament because of injury and was given a wild card into this year’s field, faces No. 8 seed Grigor Dimitrov of Bulgaria in one of the headline matches of the first round. Wawrinka, a three-time major titlist, eliminated Dimitrov in the first round at Wimbledon in June.

Nadal’s half of the draw includes No. 3 seed and 2009 U.S. Open champion Juan Martin del Potro — who could face another former U.S. Open champion in Andy Murray in the third round — and fifth-seeded Kevin Anderson, the Wimbledon and U.S. Open runner-up.

Besides Federer-Djokovic, the other possible men’s quarterfinals are Nadal-Anderson, Del Potro-Dimitrov and Zverev-Cilic.

Women’s No. 2 seed Caroline Wozniacki faces 2011 U.S. Open champion Sam Stosur in the first round. Sloane Stephens, the defending champion, is the No. 3 seed and could face former No. 1 Victoria Azarenka in the third round.

Potential women’s quarterfinals include Halep vs. No. 8 Karolina Pliskova, Wozniacki vs. No. 5 Petra Kvitova, Stephens vs. No. 7 Elina Svitolina, and No. 4 Angelique Kerber vs. No. 6 Carolina Garcia.