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Boxing icon Ali passed away at the age of 74 on Friday after a three-decade-long battle with Parkinson's disease.
Tributes have poured in from around the globe as people pay respect to the three-time world heavyweight boxing champion, widely regarded as one of the finest sportsmen in history.
A noted sports fan, Mandela was quoted in 1990 saying his only regret in life was "that I never became the boxing heavyweight champion of the world".
When Mandela died in 2013, Ali hailed the former South African president's legacy, with both men doing so much in their lives to break down racial barriers in their home countries.
Ali said: "He inspired others to reach for what appeared to be impossible and moved them to break through the barriers that held them hostage mentally, physically, socially and economically."
And a statement from the Nelson Mandela Foundation released on Saturday read: "Ali was a legend, both as a sporting great and as a public figure willing to make sacrifices for his beliefs. He will be missed around the world.
"It was no accident that a photograph of the two men together was positioned right next to Madiba's desk in his office at the Nelson Mandela Foundation.
"Nor is it surprising that in Madiba's latter years his favourite book at the office was an autographed copy of the outsize Ali biography, 'Greatest of All Time'."
Foundation CEO Sello Hatang added: "Nelson Mandela, a boxing enthusiast most of his life, acknowledged Ali as his boxing hero.
"Madiba had great respect for his legacy and spoke with admiration of Ali's achievements."