Maria Sharapova easily reached the third round of the Qatar Open, dispatching the French qualifier Caroline Garcia 6-3, 6-2.
The third-ranked Russian, who won the tournament in her two previous appearances, broke Garcia twice go up 3-0 in the first set.
Garcia won the next two games but Sharapova then broke for a third time. The second set went with serve until Sharapova broke to go up 4-2, and she clinched the victory when the Frenchwoman hit a forehand long.
Sharapova was joined in the third round by the 11th-ranked Marion Bartoli, who downed the former French Open champion Francesca Schiavone 7-6, 6-3.
The Belarusian has only beaten the American once in 12 attempts but has her thoughts prepared for twin scenarios which could cause her significant setbacks in Doha.
Williams only needs to win three matches to regain top spot, and might also fancy herself to take away Azarenka's title if they meet in Sunday's final.
"Well I'm not happy about it," Azarenka, who retained her Australian Open title last month, said of her poor record against Williams. "But I don't really think about it that way anyway. It's in the past, and I never really look in the past. I make room for new memories in the future you know – to have my full focus, my full attention, to live in the present and in the future."
The immediate future suggests a last 16 meeting with Dominika Cibulkova, the tenacious Slovakian, a quarter-final with Sara Errani, the vastly improved Italian, and a semi-final against Agnieszka Radwanska, the world No 4 from Poland.
An encounter with Williams could affect the positive mindset that Azarenka has developed since winning the first of her two Australian Open titles 13 months ago, but she declared she is unaffected.
"For me It doesn't matter if I have to play Serena in any tournament. I would love to play her on any given day," she said. "I think she is a great champion and a great challenge to have."
Azarenka added that winning titles was more important to her than the No 1 spot, which to her is "just a bonus" that comes with success.
"Whoever is in front of me, I'm trying to beat them," she said.
Another player who could take away Azarenka's top spot this week is Sharapova, although that would require Azarenka to fail to reach the final and Williams to fail to reach the semi-final.
The Russian said: "It certainly makes for an exciting storyline, but from a personal perspective, you know, the further you go in the week the better chance you give yourself to regain that ranking.
"It will also be depending on other players' results, so it's tough to focus on it [the No 1 ranking] too much. I think all of us will be focusing on just taking one step at a time."
Follow us @SprtNationalUAE