Williams returned from giving birth to her first child to reach the 2018 Wimbledon and US Open finals, but suffered upset losses in both to leave her stuck on 23 major wins.
Rafael Nadal won a record-extending 11th French Open title in June and reached the semi-finals both at Wimbledon and the US Open.
Djokovic has won his last four meetings with Federer and now leads the Swiss 25-22 overall.
Roger Federer defeated Italy's Fabio Fognini 6-4, 6-3 as the Swiss great moved three wins away from his 100th career title.
Andre Agassi previously coached Novak Djokovic from the 2017 French Open until they split in March this year.
Rafael Nadal was forced to withdraw from his US Open semi-final against Juan Martin del Potro in early September with a knee injury.
Djokovic can regain top spot from Rafael Nadal this week if he betters the Spaniard's performance in the French capital.
Nadal dominated the singles charts with 7,660 points, and Halep remained No. 1 in the WTA rankings despite being down with a back injury.
Gerard Pique believes Rafael Nadal and Novak Djokovic will both play in the reformed Davis Cup next year and has said the door remains open to Roger Federer.
Rafael Nadal headlines the list of players expected to compete at the 2019 Mexican Open in the Pacific resort city of Acapulco.
Djokovic climbed one spot up to second after claiming the Shanghai Masters title for the fourth time in a row.
Novak Djokovic has now been victorious in 18 ATP matches in a row and in recent months won Wimbledon, the Cincinnati Masters, the US Open and now Shanghai for a fourth time.
The 17-time Grand Slam champion has also given shelter to the flood victims in his tennis academy.
The Serbian second seed beats Marco Cecchinato, whom he had lost to in the French Open quarter-finals earlier this year.
Fernando Verdasco has not commented on the incident when he aggressively gesticulated at a ball boy to hurry up during last month's Shenzhen Open in China.
Novak Djokovic and Rafael Nadal have played 52 times against each other with the Serb leading their head-to-head 27-25.
Roger Federer remains behind Nadal with 6,900 points. And in the WTA rankings, Japan's Naomi Osaka jumped two positions to the fourth spot.