Ali, arguably the most prominent U.S. Muslim, on Wednesday released to The Associated Press a letter he wrote to supreme leader Ayatollah Ali Khamenei in February.
The letter asks Khameini to release Josh Fattal and Shane Bauer, who were arrested while hiking in northern Iraq near the Iranian border. A third hiker, Sarah Shourd, was released on bail in September.
"Please show the world the compassion I know you have in your heart," he wrote, asking Khamenei as a brother in Islam to show the same mercy and compassion for the two men as he did for Shourd.
Ali also wrote a letter to Khamenei shortly before Shourd was released, though it was unclear whether it had any effect.
The 69-year-old is the founder of a center for world peace in Louisville, where he grew up and launched a boxing career that included three world heavyweight titles.
His wife, Lonnie Ali, told the AP in a telephone interview from their Arizona home that her husband was asked to intervene by the late John Arum, son of boxing promoter Bob Arum.
John Arum, also a hiker, died on Storm King Mountain in Washington state shortly after he asked Ali to help and before Shourd was released, she said.
Lonnie Ali said her husband has visited Iran twice before, including a trip in the early 1990s where he tried to secure the exchange of prisoners during the Iran-Iraq war.
She said he would be willing to go to Iran to help secure the hikers' release, but it would depend on his health. Parkinson's Disease has limited his speech and movement.
"Life is sacred; we just want to make sure Muhammad is physically up to such a trip," she said.
Lonnie Ali said Alex Fattel, Josh Fattel's brother, had visited the Alis in Arizona on Tuesday.
"We are deeply grateful to Mr. Ali and the many other people around the world who know that Shane and Josh absolutely do not deserve to be in prison," the families said in a statement released through their spokeswoman, Samantha Topping. "We hope and pray that Iran hears this appeal and responds with compassion. It is time for this nightmare to end."