In Friday's quarterfinals, Robredo, who is the sixth seed, beat No. 14 Jarkko Nieminen of Finland, 6-7 (4-7), 7-6 (7-4), 6-4. The fourth-seeded Davydenko was a 6-3, 6-3, winner over No. 9 Mario Ancic of Croatia.
Ancic, who won the St. Petersburg Open in Russia last week, needed a victory in Paris to qualify for the upcoming Tennis Masters Cup in Shanghai.
The loss ended his 2006 season.
Both Davydenko and Robredo have qualified for the season-ending ATP Tour tournament. They will meet in one of Saturday's semis.
The other semi pits Haas against Hrbaty.
Notable deaths of 2014 [PHOTOS]