Thiem will overtake Roger Federer for the No. 3 spot in the world if he beats Mager.
Mager or Thiem will face the winner of the match between Spain's Pedro Martínez Portero and Hungary's Attila Balazs. Portero led 6-2, 2-2 when the match was suspended.
Third-seeded Christian Garin of Chile and fifth-seeded Borna Coric of Croatia set up a semifinal match. Garin beat Argentina's Federico Coria 2-6, 6-3, 7-5, and Coric topped Italy's Lorenzo Sonego 7-6 (5), 6-3.