The boxer refused to be inducted into the U.S. Army in 1967, claiming conscientious objector status, and was sentenced to five years in prison.
On Friday morning, after Trump mentioned his interest in pardoning Ali, Ali's lawyer Ron Tweel responded with some pertinent information that the president may have been missing.
Trump has been on a clemency kick of late, using his near-limitless power to pardon a growing list that includes a former White House aide, a conservative commentator and a former sheriff convicted of violating a judge's orders who campaigned with Trump in 2016. The U.S. Supreme Court overturned his conviction in 1971. Mr Trump also recently said he has the "absolute right" to pardon himself in the Russian Federation inquiry, although he insists he has done nothing wrong.
The president told reporters he's looking at "thousands of names" of people who could be granted clemency because they were treated unfairly or their sentences are too long.
"I think [Trump] probably was a fan of Ali and he thought he would say something positive about him".
And for such future grants of presidential power, Trump said he may seek the recommendations of pro football players and other athletes who have protested racial injustice by kneeling during the national anthem. Ali visited the families of American and Vietnamese servicemen still missing from the war, almost three decades after he was convicted of draft evasion for refusing to fight on the battlefields.
Pardons have been at the front of President Donald Trump's mind lately. He was convicted in the 1960s of refusing compulsory military service, but the conviction was overturned by the Supreme Court in 1971.
Ali was an Olympic gold medalist in 1970 and the world heavyweight boxing champion in 1964, standing tall as an American icon. "And if I find and my committee finds that they're unfairly treated, then we will pardon them or at least let them out".
Trump's musing about an Ali pardon was blasted by the Rev. Al Sharpton, who accused the president of "nothing more than grandstanding". So does the boxing legend need a pardon?
Mr Trump pardoned her after Kim Kardashian took up her case and visited Mr Trump in the White House.
He also issued a pardon to Dick Cheney s former chief of staff Lewis "Scooter" Libby, who was convicted of lying to the Federal Bureau of Investigation in connection with the leak of a Central Intelligence Agency operative s identity.