The second-ranked Williams will move up if she reaches the semifinals of the tournament, which starts Monday and features nine of the top 10 players. The 31-year-old American would be the oldest woman to reach No. 1.
Chris Evert held the top ranking in 1985 just shy of her 31st birthday.
At the Australian Open, Williams looked dominant at times but lost in the quarterfinals to 19-year-old American Sloane Stephens. She got banged up along the way, injuring her right ankle in her first-round victory against Edina Gallovits-Hall and her back against Stephens.
Williams said she was "feeling a little better" and that neither her back nor her ankle was bothering her at the moment.
"You know, just taking it one day at a time, basically," she said. "So I will see how I feel after my first match."
Williams lost the No. 1 ranking to Caroline Wozniacki in 2010 and tumbled down the rankings because of a series of health problems. But she has played some of her best tennis in the past year, winning Wimbledon, Olympic gold, the U.S. Open and the season-ending WTA championships. She lost only one match in 2012 after her first-round exit at the French Open.
If Williams falters in Doha, top-ranked Victoria Azarenka can stay at No. 1 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.
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Williams would likely face former second-ranked player Petra Kvitova of the Czech Republic in the quarterfinals. She has an opening-round bye and will play Anabel Medina-Garrigues of Spain or Russian qualifier Daria Gavrilova in the second round.
"It will be great. I think it will be a great feeling," Williams said of returning to No. 1. "I obviously want it, but it's not the only thing I want, so if it happens, great. If not, I won't miss anything, I don't think."
Azarenka didn't want to talk about her own ranking, but she agrees a three-way race for No. 1 raises the profile of women's tennis.
"I think it's exciting. Twitter and Facebook is blowing up, so we have a lot of questions," Azarenka said. "But I think it's important also for the players to keep that competitive spirit, to kind of be on the watch out. For me, it's just extra motivation, really, to have that living and playing in this era of such competitive tennis, women's tennis. So many great girls are really stepping up their game. I feel we can see a lot of elevation in the women's game."
The defending champion in Doha, Azarenka will be looking to maintain the momentum of her second consecutive Australian Open title. But to do that, she might have to beat Williams in the final -- a daunting prospect considering their recent results. Azarenka is 1-11 against Williams, the last matchup a three-set loss in the U.S. Open final.
"Well, I'm not happy about it," she said of her record against Williams. "I mean, that's for sure. 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, to have my full focus, my full attention to live in the present and in the future."
Press; By MICHAEL CASEY]
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