The 32-year-old nose tackle refused to take a pay cut and negotiations broke down over guaranteed money, Rand Getlin of NFL Network reports.
Soliai recorded 22 tackles and a fumble recovery in 2015. He was set to earn $5.5 million in 2016, three years into a five-year, $32-million contract.
Originally drafted by the Miami Dolphins, Soliai is reportedly comfortable testing the open market, as 3-4 defenses are historically willing to overpay for reliable nose tackles.
Under Dan Quinn, the Falcons have moved to a 4-3 scheme, limiting Soliai's effectiveness.