World number two Garbine Muguruza suffered a fitness scare ahead of this month's Australian Open when she was forced to retire from the Brisbane International with severe cramping.
Simona Halep will be officially confirmed World No.1 next week when the latest rankings are released.
Garbine Muguruza officially became world number one for the first time on Monday.
Five tennis players have a chance to grab the world No 1 ranking at this week's Cincinnati Open.
Women's singles champion Garbine Muguruza asked 19-time Grand Slam winner Roger Federer to dance at the Wimbledon Champions' Dinner.
Muguruza overwhelmed Williams with a supreme display of power hitting in 77 minutes on Centre Court to become only the second Spanish woman to win Wimbledon.
Wimbledon 2017 Highlights: Garbine Muguruza stormed to her first Wimbledon title with a majestic 7-5, 6-0 victory over Venus Williams in the final.
Garbine Muguruza beat Magdalena Rybarikova 6-1, 6-1 in just 64 minutes.
World No. 11 Venus, beaten in this year's Australian Open final, was knocked out in the 2016 semi-finals and is chasing a first major title since winning Wimbledon in 2008.
Kerber, who lost to Serena Williams in the final 12 months ago, has failed to make the last eight at any of this year's three Grand Slams.
Nine-time Roland Garros champion stays on course for 10th title, women's defending champion shown the door.
Nadal began his pursuit of a record 10th French Open title with an easy win over Benoit Paire as Djokovic brushed aside Marcel Granollers to reach the second round.
Coco Vandeweghe, who had knocked out top seed Angelique Kerber in the fourth round, defeated Garbine Muguruza 6-4, 6-0 to reach the Australian Open semis
French Open winner Garbine Muguruza welcomed the fact that a new face was at the top of women's tennis rankings, after Angelique Kerber broke Serena Williams' 186-week dominance
Andy Murray had the chair umpire demand fans cut their chatter early in his second round US Open win against Spain's Marcel Granollers as the noise was becoming too big a distraction
Novak Djokovic and Rafael Nadal had little difficulty to win their respective first round matches at US Open. However, Djokovic had an arm injury scare