Filipovic first broke the news to a Croatian sports show Tuesday.
Both fighters have struggled as of late, combining for zero wins in their last four contests.
Following the third-round loss to Schaub at UFC 128 in March, Dana White speculated it was time for the 36-year-old to retire. The UFC president has softened his stance since, saying, "I owe him another fight."
Nelson (15-6) is looking to avoid dropping three straight fights for the first time in his career. Winner of the tenth season of "The Ultimate Fighter" reality series, the former IFL champion won his first two fights in the UFC before coming up short in decision losses to Junior dos Santos and Mir.
White was particularly critical of Nelson's performance against Mir at UFC 130 in May, calling it both "terrible" and "embarrassing." Nelson was visibly winded early in the fight but was diagnosed with walking pneumonia.
Brett Okamoto covers mixed martial arts for ESPN.com.