MADRID, Spain - Former No.1s Simona Halep and Angelique Kerber are in the hunt for Naomi Osaka's No.1 ranking this week at the Mutua Madrid Open. To have a chance of overtaking Osaka, Halep and Kerber will need to win the Madrid title. 

[UPDATE: Kerber withdrew from the tournament after her first round win due to an ankle injury sustained in practice]

World No.2 Petra Kvitova is the defending champion in Madrid. Despite closing the gap on Osaka's point lead by winning Stuttgart, Kvitova cannot add to her point total this week. 

Here are the No.1 Scenarios:

- Osaka, who won her first career main-draw match at Madrid on Sunday, lost in the first round last year. She can secure the No.1 ranking outright by advancing to her second consecutive clay semifinal.

- Halep, a two-time champion in Madrid and quarterfinalist last year, is defending 215 points. She will need to win the title, with Osaka losing before the semifinals.

- Kvitova will need to at least reach the final to have a chance at staying at No.2.

Coming into Madrid, Osaka has held the No.1 ranking for 15 consecutive weeks, since overtaking Halep by winning the Australian Open in January. Halep has come within one win of retaking the ranking last month at the Miami Open but lost to No.5 Karolina Pliskova in the semifinals. 

This post has been updated to reflect Angelique Kerber's withdrawal.