Justine Henin is likely to be favourite to win the Australian Open but Serena said she believes she could retain the trophy.
World number eight Caroline Wozniacki pulled out of her first match at the Sydney International with a wrist injury on Monday.
World number one Dinara Safina overcame a gutsy fightback from Lucie Safarova to beat the unseeded Czech 6-0, 4-6, 6-3 and seal a place in the last eight of the Madrid Open on Thursday. Top seed Safina will play Alona Bondarenko on Friday for a place in the last four after the Ukrainian beat Russian Anna Chakvetadze 6-0, 2-6, 6-3 earlier in the day.
Top seeded pair of Sania Mirza and Martina Hingis suffered their second defeat since joining forces, losing 7-6(5), 3-6, 9-11 to Bethanie Mattek-Sands and Lucie Safarova, at the Madrid Masters Open on Thursday.
World number one Roger Federer moved closer to a Sony Ericsson hat-trick on Monday, easing into the fourth round of the Masters Series event with 7-5 6-3 win over Spain's Nicolas Almagro.
Russian Nadia Petrova ended Lucie Safarova's brilliant run at the Paris Open when she outfoxed the Czech 4-6, 6-1, 6-4 in Sunday's final
China's Na Li kept the Asian interest alive as she beat ninth seed Dinara Safina 6-2, 6-2.
Mauresmo stayed on course to defend her Australian Open title with a 6-3, 6-1 win over Czech Eva Birnerova in the third round on Friday.
Former world number one Martina Hingis' first comeback tournament ended in the semi-finals when she was beaten by fourth seed Flavia Pennetta 1-6, 7-6, 6-2 at the Australian hardcourt championships on Friday.
Despite Venus' misguided advice, Serena Williams beat Lucie Safarova 6-3, 3-6, 7-6.
Venus Williams beat Czech Lucie Safarova 6-1, 6-4 in the second round of the Italian Open
Top seed Nadia Petrova fired five aces in securing her 22nd victory of the year at the Amelia Island tournament.
The Czech teenager beat Italian fourth-seed Flavia Pennetta in the final of the Australian women's hardcourt championship.
The third seeded Indian beat Israel's Shahar Peer 7-6, 6-1 at the Forest Hills Women's Classic in New York.
Third seed Jelena Jankovic had to work very hard on Friday to quell the challenge of Czech Lucie Safarova 5-7 7-6 6-2 and reach the fourth round at Wimbledon.
American Bethanie Mattek-Sands, whose agonising on-court injury shocked Wimbledon, says she will need surgery and faces being sidelined from the game.
The third seed, who lost to Lucie Safarova, was richer by $12,000.
Serena Williams backed the searing Perth conditions as perfect preparation for her Australian Open title bid but the weather proved too hot for Canadian Eugenie Bouchard.
World number one Karolina Pliskova needed just 46 minutes to defeat American Jennifer Brady 6-1, 6-0 at Arthur Ashe Stadium and punch her ticket to the quarter-finals at the US Open on Monday.
French Open champion Stanislas Wawrinka has moved up five places to number four in the official ATP world rankings released on Monday.
Hot favourites Sania Mirza and Martina Hingis fell by the wayside at the French Open, beaten by seventh seeds Bethanie Mattek-Sands and Lucie Safarova in the quarter-finals of the women's doubles
Mattek-Sands was playing Romania's Sorana Cirstea on outside Court 17 when she appeared to slip as she approached the net at the beginning of the third set then collapsed awkwardly to the grass.
Indian ace Sania Mirza and Switzerland's Martina Hingis entered the semi-finals of the WTA Finals after beating Taiwanese combination of Hao-Ching Chan and Yung Jan Chan 7-6 (12-10) 7-5 in Singapore on Friday. The Indo-Swiss pair will be pitted against the winner of the match between top seeds Caroline Garcia-Kristina Mladenovic and Bethanie Mattek-Sands- Lucie Safarova. It was a hard-fought two sets where both the teams held their service game till they reached 5 games all. It was in the 11th game of the first set that Sania and Hingis were broken. But the joy of their opponents was shortlived as they broke back in the very next game to take the first set into a tie-breaker.
World No 1 Williams, 33, could not practise on Friday, still suffering from an illness that left her coughing and spluttering during her three-set semi-final win over Swiss Timea Bacsinszky.
Spain's Garbine Muguruza moved to the brink of the WTA Finals last four with a 6-4, 6-4 win over Angelique Kerber on Wednesday after Petra Kvitova opened her account with a 7-5, 7-5 victory over fellow Czech Lucie Safarova.
Rohan Bopanna gained three places to be world number 21, and is now country's top ranked player in the ATP doubles chart.
Maria Sharapova remained on course for consecutive Madrid Open titles when she recovered from dropping the second set to beat Caroline Wozniacki 6-1, 3-6, 6-3 on Thursday and book a spot in the semi-finals.
As the world No 2 women's player focuses on the next big Grand Slam, Wimbledon, Rediff.com takes readers through her glamorous life via her instagram posts.
Garbine Muguruza made an imposing start to the WTA Finals by confidently swotting aside Czech Lucie Safarova 6-3, 7-6 (4) in their White Group opener on Monday.
India's tennis star Sania Mirza retained her numero uno status in women's doubles for the second consecutive year, despite failing to defend the WTA Finals Singapore title with partner Martina Hingis. Defending champions Sania and Hingis had lost to Ekaterina Makarova and Elena Vesnina in the semi-finals of the WTA Finals Singapore on Saturday.
Maria Sharapova is renowned for her sheer determination in the face of adversity but in Singapore on Saturday, the Russian was quick to cast doubt over her chances of winning the WTA Finals after an injury-ravaged second half of the season.
Russians Ekaterina Makarova and Elena Vesnina won the Wimbledon women's doubles title for the first time, while Poland's Lukasz Kubot and Brazil's Marcelo Melo won the Wimbledon men's doubles crown.
American tennis ace Venus Williams has entered the top ten of latest WTA ranking following her victory in the Zhuhai Masters in China.
Venus Williams avoided another early exit with a routine win over fellow American Alison Riske at the Volvo Car Open in South Carolina while Swiss second seed Belinda Bencic was ousted by Russian qualifier Elena Vesnina.
Pliskova, a finalist at last year's US Open who reached the semi-finals at Indian Wells last week, relied on her booming groundstrokes and strong returning to dispatch her American opponent in 59 minutes.
Garbine Muguruza continued her dream debut at the WTA Finals by completing round robin play with a perfect 3-0 record to advance to the semi-finals after a hard fought 6-4, 4-6, 7-5 victory over Petra Kvitova on Friday.
Defending champion Petra Kvitova used a dominant serve to beat Lucie Safarova 6-7(6), 6-2, 6-2 in their all-Czech final at the Connecticut Open on Saturday.
Following is a list of American Serena Williams' 22 grand slam singles titles as she equalled Steffi Graf's professional era record with victory at Wimbledon on Saturday
Following Iga Swiatek's victory over Coco Gauff in the final, here's a list of French Open women's singles champions:
Angelique Kerber displayed her grit and vaunted fitness as she battled back to beat France's Pauline Parmentier 7-5, 3-6, 7-5 in scorching heat on Monday to reach the fourth round of the BNP Paribas Open.