- Venus Williams sets sights on No. 1 ranking for the first time in 10 years
- Williams beat Sara Errani to reach the Cincinnati Masters quarterfinals
- Younger sister Serena also into the last eight after beating Urszula Radwanska
- Defending U.S. Open champion Sam Stosur and Czech Petra Kvitova also advance
When Venus Williams was knocked off the top of the women's tennis world rankings by younger sister Serena in July 2002, she couldn't have imagined that over a decade later she would still be waiting for a return to the summit.
Despite winning three further Wimbledon singles titles since last being No. 1, the American has endured a 10-year spell blighted by losses of form and fitness -- culminating in being diagnosed with Sjogren's Syndrome at last year's U.S. Open.
But the 32-year-old is on the comeback trail, setting her sights on a return to the top of the world -- plus singles and doubles glory at Flushing Meadows -- after Thursday's third-round win over French Open runner-up Sara Errani at the Cincinnati Masters.
"Before all my injuries and illnesses I was No. 2 in the world and Serena was No. 1, and we were No. 1 in doubles," the seven-time grand slam winner, now ranked 64th, told reporters.
"We were literally on top of the world until a lot of things came crashing down on us. I'd like to work my way back. Of course that's a dream for me.
"I dream of those things. That's why I'm here, because I feel like I still have it. It's one match at a time, pretty much."
Williams' reward is a quarterfinal match against third seed Sam Stosur, the Australian who beat Serena in an ill-tempered 2011 U.S. Open final to claim her first grand slam title.
While Venus is trying to recapture her best form, younger sister Serena is the dominant force in women's tennis.
The world No. 4 won a fifth Wimbledon title last month before returning to Centre Court to destroy Maria Sharapova in the Olympic women's singles final at London 2012.
The 14-time major winner continued her imperious run of form by battling past a stubborn Urszula Radwanska 6-4 6-3.
After the match, Serena spoke of fondness for the Pole, whose older sister Agnieszka is top seed for the hard-court tournament and reached the last eight with a three-set win over American teenager Sloane Stephens.
"I think they're both great players, and great sisters," the 30-year-old said as she continued her quest for a first Cincinnati title. "I absolutely love seeing another pair of sisters doing so well on the tour.
"Urszula has worked really hard, and me being a younger sister and Urszula being a younger sister too, I'm always looking for her to do well and I hope she does really well.
"Her game is great. What's best about her game is she's like her sister -- she doesn't do anything badly. Those are always tough opponents to play."
Serena's next opponent is German fifth seed Angelique Kerber, who advanced courtesy of a 6-4 7-6 (7-5) defeat of Czech qualifier Andrea Hlavackova.
Also safely through is 2011 Wimbledon champion Petra Kvitova. After picking up her first title of 2012 in Montreal on Monday, the world No. 5 continued her winning run by beating China's Peng Shuai 6-2 6-2.