"A couple of times it went through my mind," she said. "On the other hand, I thought I don't want to quit in my last time at the Australian Open.
"I said in my mind, keep fighting. You never know what happens on the other side of the court."
No. 2-ranked Rafael Nadal dealt with his own injury problems Sunday. Playing with his right knee heavily strapped, the 2009 champion had his left ankle taped during the first set against Feliciano Lopez. He won the match 6-4, 6-4, 6-2 and afterward said he was "fine."
Clijsters was hurt in the first set while serving at 3-all and 30-all. As she hit a forehand, her left foot got stuck on the surface and the ankle twisted awkwardly.
She got up to finish the point but then immediately called for the trainer and had the ankle strapped.
Clijsters' movement was clearly slowed when she resumed. But the injury seemed to affect Li just as much. The 29-year-old Li, the first player from China to win a Grand Slam singles title, looked increasingly stressed as the match progressed.
She looked desperately at her husband, also her coach, in the stands more and more regularly.
After 2 hours, 23 minutes, Li netted a backhand to put Clijsters through to a match against either top-seeded Caroline Wozniacki or Jelena Jankovic.
Victoria Azarenka was the first player to reach the quarterfinals when she beat Iveta Benesova 6-2, 6-2.
The third-seeded Belarusian is yet to drop a set at the tournament and will next meet eighth-seeded Agnieszka Radwanska, who beat Julia Goerges of Germany 6-1, 6-1.
With the win, 22-year-old Azarenka stayed in the hunt for the No. 1 ranking. Petra Kvitova and Maria Sharapova can also claim the top spot from Caroline Wozniacki.
"I would be a liar if I said I didn't care about it," Azarenka said. "It's in the back of my head and we'll take it day by day, I guess."
Nadal, who bizarrely hurt his knee while sitting in a chair the day before the tournament began, is one win away from a possible semifinal against old rival Roger Federer after beating his friend Lopez for the ninth time in 11 matches.
"Feliciano is one of my best friends on tour. That's the game. That's the sport," said Nadal, who hasn't dropped a set in four matches. "You understand that's only a game. You understand that everybody wants to win; everybody wants to finish the match with the best result."
On a sunny day with the temperature rising to 33C (91F), both players sat with ice towels around their necks during the changeovers.
Nadal needed treatment from the trainer for a left ankle problem after three games of the first set. By that time, he had already broken serve and he did the same early in the next two sets to maintain control against Lopez.
"I am fine," Nadal said. "It was a very, very hot day. I think it's positive to keep winning in straight sets."
Nadal plays Tomas Berdych next, hoping to avoid a third straight quarterfinal loss in Melbourne. Defending the title in 2010, the Spaniard retired with a knee injury against Andy Murray. A year ago, he was hampered by a hamstring problem in a straight-sets loss to David Ferrer.
"Hopefully not happen this time," Nadal said. "I had a bad experience last two years here. It's tough have to go out of a tournament like Australia in quarterfinals."
Berdych beat Nicolas Almagro of Spain 4-6, 7-6 (5), 7-6 (3), 7-6 (2).
Federer was to play 19-year-old Australian Bernard Tomic in the first match of the night session later Sunday. The 16-time Grand Slam champion hasn't been beaten by a teenager since 2006, when he lost to Andy Murray at the Cincinnati Masters.
- AP