Victoria Azarenka, the top-seeded player left in the women's draw after Caroline Wozniacki, Kim Clijsters and Vera Zvonareva were eliminated, defeated unseeded Russian Ekaterina Makarova 6-2, 6-3 to reach French Open quarter finals.
She will now face Li, who had earlier become the first player from China to reach the Roland Garros quarter finals with a disjointed 2-6, 6-1, 6-3 defeat of 21-year-old Czech ninth seed Petra Kvitova.
Despite her superior seeding, Azarenka has beaten Li just once in four attempts - most recently losing in the last 16 at the Australian Open - and has never gone beyond the quarter finals at a Grand Slam.
"I'm in a different chapter of my career," said Azarenka.
"It's going to be a different quarter final for me. But I'm feeling really confident and I'm really looking forward to it."
Having broken Makarova's serve at the first attempt, Azarenka conceded the break with a double-fault in the next game but then broke again to go 4-2 up when Makarova clipped a forehand into the tramlines.
The Belarusian took the first set with a backhand return winner and there were four breaks of serve apiece in the second set before a long forehand from Makarova handed Azarenka what proved to be the decisive break.
Azarenka converted her first match point when Makarova put a forehand beyond the baseline, sending the world number four into the last eight at a Grand Slam for the fourth time in her career.