Venus is in her 11th Australian Open campaign but is yet to win the singles crown, in stark contrast to Serena.
She faces Li next after the 16th seed upset Danish fourth seed Caroline Wozniacki 6-4, 6-3.
Tsonga won a thriller against Spanish 26th seed Nicolas Almagro, 6-3, 6-4, 4-6, 6-7 (6/8), 9-7.
She said she could break her Australian drought this year.
“I have always had some great battles with Lleyton, he’s a champion and has the ability to make you nervous in a match.”
The Russian sixth seed ensured he stayed alive by coming through a marathon five-setter against Spanish ninth seed Fernando Verdasco, prevailing 6-2, 7-5, 4-6, 6-7 (5/7), 6-3.
Li is looking forward to meeting Venus, who she beat in their only previous match at the 2008 Beijing Olympics.
Her victory broke new ground for Chinese tennis with the 27-year-old joining compatriot Zheng in the last eight, the first time two Chinese players have reached that stage of a Grand Slam.
Like Federer,mbt reviews, women’s defending champion Serena Williams was a class apart as she devoured Australia’s Sam Stosur 6-4, 6-2.
“I think the first two sets I was very dominant on the court, then he lifted up his level of the game a little bit,” he said.
They join Li, Justine Henin, Nadia Petrova, Maria Kirilenko and Zheng Jie in the last eight.
She will play seventh seed Victoria Azarenka as she guns for a fifth title after the Belarrussian beat ninth seeded Russian Vera Zvonareva 4-6, 6-4, 6-0.
“I’m in for a good match for sure. I favour my chances in a best-of-five set match. We’ll see how it goes,” Federer said of Davydenko, while paying tribute to Hewitt.
“It’s important when you’re playing a local girl to not let the crowd get too involved or else they’ll kill you,” she added. “That was the plan, to not let them get involved.”
Djokovic was impressive in his rout of Kubot.
Federer, Williams sisters stride into tennis Open quarters
A dominant Roger Federer joined the Williams sisters in the Australian Open quarter-finals Monday while Li Na ensured China has two players in a Grand Slam last eight for the first time.
Third seed Novak Djokovic, the 2008 winner, also progressed with an emphatic 6-1, 6-2, 7-5 win over Poland’s unseeded Lukasz Kubot and will next meet French 10th seed Jo-Wilfried Tsonga, who he beat in the 2008 final.
The world number one Swiss shattered the hopes of local fans by crushing Lleyton Hewitt 6-2, 6-3, 6-4 for his 15th consecutive win over the Australian 22nd seed.
“It’s really good to match my game against her serve, because she’s one of the best servers on the tour,” Williams said of Stosur.
Her sister Venus, seeded six, found the going tougher against Italian 17th seed Francesca Schiavone, losing the first set before bouncing back for a 3-6, 6-2, 6-1 win.