The track, which features rapper Drake, is currently number one in the midweek charts, according to the Official Chart Company.
What's My Name was released way back in November but is slowly making its way to the top of the charts.
If Rihanna manages to bag that number one spot on Sunday, it will be her fifth single to reach the top spot, after Umbrella, Take A Bow, Run This Town and Only Girl (In The World).
This would make her the first solo female artist to score five number one hits in consecutive years.
Elvis Presley is the only other solo artist who has managed to achieve this feat.
Cardle's debut single When We Collide - a cover of Biffy Clyro's Many of Horror - has been number one since Christmas.
The track is now number two in the midweek chart.
Meanwhile, Plan B looks set to return to the top of the UK album charts after eight months as his LP, The Defamation Of Strickland Banks is currently number one while Rihanna's Loud is in second place.
She will definitely make UK history. Because if WMN can't do this than her other singles will do it.
Late this year, she just need to make another Xfactor Performance then she her single would go straight to no.1