Officials said they will try to get the four quarterfinals and both semifinals in Friday so the tournament can conclude as scheduled with a final Saturday.
Seppi, at No. 3 the highest seed left in the field, is to go against seventh-seeded Philipp Kohlschreiber in the quarterfinals with a match between Denis Istomin and Ryan Harrison also set in that half of the draw.
The other quarterfinals have sixth-seeded Andy Roddick facing Fabio Fognini and Marinko Matosevic playing Steve Darcis.
Celebrity Families of 2014 [PHOTOS]