Djokovic, who is the defending champion and seeded No. 1, could meet 13-time champion Nadal in the quarterfinals at Roland Garros. Djokovic beat Nadal in the semifinals a year ago.
In the women's draw, No. 1 Iga Swiatek, the 2020 champion who enters the French Open on a 28-match winning streak, could face two-time major runner-up Karolina Pliskova in the quarterfinals and either Paula Badosa or Aryna Sabalenka in the semifinals. Possible quarterfinal matchups in the other half of the draw include defending champion Barbora Krejcikova, the No. 2 seed, against No. 5 Anett Kontaveit and No. 4 Maria Sakkari vs. No. 6 Ons Jabeur.
Nadal leads the Grand Slam title standings among men with 21, one ahead of Djokovic and Roger Federer. This will be Djokovic's first major tournament since last year's US Open; he was not allowed to play in the Australian Open because he has not been vaccinated against COVID-19.
If that Djokovic-Nadal showdown happens, the winner could face No. 6 seed Alcaraz in the semifinals. Alcaraz, 19, recently won the Madrid Open on clay and became the youngest man to break into the top 10 in the rankings since Nadal in 2005. Alcaraz could meet No. 3 seed Alexander Zverev in the quarterfinals.
The potential quarterfinals in the other half of the bracket are No. 2 Daniil Medvedev against No. 7 Andrey Rublev in a matchup between two Russians who will not be allowed to compete at Wimbledon because of that country's invasion of Ukraine, and 2021 runner-up Stefanos Tsitsipas against No. 8 Casper Ruud.
Osaka is a four-time Grand Slam champion who used to be No. 1 in the rankings but has slipped to No. 38 in part because of a lack of activity. That included time off for a mental health break after she withdrew from Roland Garros ahead of her second-round match last year, saying she has dealt with anxiety and depression.
Because she is not seeded at the French Open, where play begins Sunday, Osaka was not safe from facing a seeded opponent right away, so that's what will happen against No. 27 Anisimova.
Anisimova won their third-round encounter at Melbourne Park in January by a score of 4-6, 6-3, 7-6 (5).
The Associated Press contributed to this report.