The second-ranked Williams will become No. 1 if she reaches the semifinals of the tournament which starts Monday and features nine of the top 10 players.
If Williams falters, top-ranked Victoria Azarenka can guarantee herself the No. 1 spot by reaching the final. Third-ranked Maria Sharapova also has a chance to return to No. 1 if she wins the tournament, Williams fails to advance to the semifinals and Azarenka doesn't reach the final.
Sharapova last held the No. 1 ranking for four weeks in 2012 after the French Open.