They're eagerly anticipating the chance to prove it at the Australian Open.
Jankovic has the bragging rights now, spending the last two months at No. 1 in the rankings despite a series of minor injuries and illnesses last year. But the 23-year-old Serb has her doubters because she has yet to win a Grand Slam - something that second-ranked Serena Williams has done nine times - and is short on match practice after coming down with an illness in Hong Kong.
"It will be an extra challenge for me,'' Jankovic said Saturday, two days before the season-opening major gets under way.
Still, she wasn't short on confidence, saying she feels she deserves the top ranking. She also undertook what she called her toughest-ever training regime in November and December, clearly adding some muscle, to help her stay on top.
"If I win a Grand Slam, it will be great result, great achievement,'' Jankovic said. "But I'm already No. 1, and I believe all of these girls here want to be where I am now. So I'm just enjoying it and really having fun. I play tennis because I like to play, not because I have to prove anything to everybody.''
Williams is ready to make her own case that nobody is better than her.
"I would feel weird sitting here saying I'm not the best,'' said a relaxed and fit-looking Williams, who won the last Grand Slam, the U.S. Open, in September while briefly regaining the top ranking. "Even if I'm ranked 100 in the world, I would sit here and say I'm the best player.
"Nothing against Jankovic. She went out in the fall and worked hard and got the No. 1 ranking. I feel like I'm the best just because I'm not going to sit here and say anyone is better than me. I shouldn't be in tennis if I felt that way.''
Both would have to overcome some serious challenges to get to the Jan. 31 final. Even with the absence of defending champion Maria Sharapova - still getting back to fitness after a shoulder injury sidelined her for most of the second half of 2008 - the women's field shapes up as one of the strongest in years.
Dinara Safina, emerging from the shadow of older brother Marat Safin, earned the third seeding by winning four tournaments last year and reaching the French Open final and the U.S. Open semis.
No. 4 Elena Dementieva, the gold medalist at the Beijing Olympics, is on a 10-match winning streak after winning two warmup tournaments, dropping only one set.
No. 5 Ana Ivanovic is only 21 but already has had a stint as No. 1, won at Roland Garros and reached the final here last year.
Like Jankovic, Safina and Dementieva are pursuing their first Grand Slam titles.
Serena's sister Venus Williams, who has won seven Grand Slam singles titles - including her fifth Wimbledon title last year - reckons she can get back to No. 1, too.
"Right now I'm not No. 1, so the number and everything isn't matching up. But I hope to get there,'' the sixth-seeded Williams said. "It's difficult to go out on the court and look across the net and think that someone might be better than you. So I try not to bring those kind of mentalities on the court.''
The big unknown is who is in the best form after tennis' brief off-season, and who took things too easy. That sets the stage for upsets and the emergence of new stars like 18-year-old Danish player Caroline Wozniacki, who held three match points against Serena Williams in Sydney last week before losing.
"The competition is very strong, and the girls are getting stronger and stronger and everybody is working hard,'' Jankovic said. "I think it's great for the game, and I think it's also great for the spectators. It's great entertainment because you never know who is going to win.''
Serena Williams agreed that the women's game has become much more competitive than the days when only three or four players were legitimate contenders. She feels she is playing better than when she was dominating the sport but has to struggle more to win.
Both Williams sisters had some bad news for any players hoping they might be considering retirement.
Serena, 27, said she hopes to be competing at a high level for "a really long time.''
"I feel like I just want to continue to get better, so haven't reached my best yet,'' she said.
Venus, 28, said she feels she's "living the dream'' and doesn't want it to end.
"When the dream's over, I'm going to think about when I was living the dream,'' she said. "The dream's still large. It's just big, huge. Like there's stuff being added to the dream. So, yeah, no end in sight.''
As for who is No. 1 right now, Jankovic said the answer will come soon enough. Any one of four women could have the top ranking on completion of the Australian Open.
"The best one will be holding the trophy at the end of the two weeks,'' she said.
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