Seau died of a gunshot wound to the chest at his Oceanside, Calif., home last week and a coroner concluded his death was a suicide, CNN reported Tuesday.
Some have speculated repeated blows to his head during his 20-year NFL career could have been a contributing factor.
Researchers have contacted his family to request they be allowed to study his brain, said Shawn Mitchell, who was Seau's pastor.
"The Seau family is currently revisiting several important family decisions and placing them on hold in order to confer with their elders," a family statement said. "All possibilities are being considered, but none will be acted upon until the Seaus arrive at an agreed-upon direction."
CNN said no evidence shows Seau suffered from chronic traumatic encephalopathy, a degenerative disease brought on by multiple concussions.
Last month, Atlanta Falcons safety Ray Easterling, the lead plaintiff in a class action lawsuit against the NFL over concussion-related injuries, committed suicide.
Easterling had symptoms of repetitive head trauma: memory lapses, anger and deep depression, family and friends said.