Novak Djokovic starts 339th week as World No. 1, Ashleigh Barty continues reign atop WTA list, Naomi Osaka drops out of top 5

Novak Djokovic and Ashleigh Barty continue to lead the world rankings, moving ever closer to achieving new milestones in the weeks ahead. But for reigning Australian Open champion Naomi Osaka, the recent on-court struggles have translated into another tumble down the rankings.

Novak Djokovic was defeated by Daniil Medvedev in the US Open final, and he is uncertain about his schedule for the last quarter of the season. Even so, the Serb has begun his 339th week at the top of the ATP rankings because of the huge points lead he has accumulated.

Djokovic is now only 39 weeks away from breaking the all-time record (including both men and women) for most weeks at world No. 1, currently held by Steffi Graf (377 weeks). Djokovic already holds the men's record, having broken Roger Federer's mark of 310 weeks earlier this year.

Novak Djokovic and Daniil Medvedev during the presentastion ceremony of the 2021 US Open

US Open champion Daniil Medvedev remains firm at No. 2 for another week. The Russian has a chance to end the season as ATP year-end world No. 1, even if Djokovic remains atop the world rankings.

With the Davis Cup qualifiers taking place last week, there were no ATP tournaments on the calendar. As a result, there are no changes in the top 30 of the world rankings.

Djokovic and Medvedev are followed in the rankings by Stefanos Tsitsipas, Alexander Zverev, Andrey Rublev, Rafael Nadal, Matteo Berrettini, Dominic Thiem, Roger Federer and Casper Ruud.

Lower down the rankings, Benjamin Bonzi climbed 15 spots to a new career-high of No. 61. The Frenchman won his sixth ATP Challenger title of the season (and his third in a row) in Rennes this past weekend.

James Duckworth also climbed 15 spots to a new career-best No. 65 after winning the ATP Challenger in Istanbul, Turkey.

Ashleigh Barty begins 94th week as World No. 1

Ashleigh Barty at the 2021 US Open

Ashleigh Barty has begun her 59th consecutive week and 94th overall week at the top of the WTA rankings list. Barty has the ninth longest reign at the No. 1 spot in women's tennis history, and looks all set to overtake Lindsay Davenport (98 weeks) for eighth spot soon.

The Australian is followed in the rankings by Aryna Sabalenka (No. 2), Karolina Pliskova (No. 3) and Elina Svitolina (No. 4).

French Open champion Barbora Krejcikova climbed two positions to a new career high of No. 5. 2020 Roland Garros champion Iga Swiatek, meanwhile, climbed two positions to No. 6.

Sofia Kenin dropped one spot to No. 7 while Naomi Osaka dropped three positions to No. 8, after points from the latter's 2020 US Open title dropped off her tally.

LIke Djokovic, Osaka is also uncertain about when she will return to tournament action next. If the Japanese doesn't play Indian Wells next month, she could be in danger of dropping out of the top 10.

Two-time Grand Slam winners Garbine Muguruza and Petra Kvitova round out the current top 10.

The players who picked up WTA 250 titles last week made big jumps in the rankings. Denmark's Clara Tauson, who won her second title of the season in Luxembourg, climbed 18 positions to a new career-high of No 52. And Italy's Jasmine Paolini climbed 23 spots to No. 64 after winning first WTA singles title in Portoroz, Slovenia.