Ali, 74, passed away on Friday following a lengthy battle with Parkinson's disease, with septic shock named as the official cause of death.
The American is widely regarded as one of the best athletes to have ever lived, and is also remembered for his humanitarian work and as a central figure in the civil rights movement in the United States in the 1960s.
And after going down to world number one Novak Djokovic in the French Open final on Sunday, Murray spoke about what Ali meant to him.
"Yeah, it was a sad day obviously yesterday," the Briton said. "You know, obviously he had been struggling for a long time physically.
"It did seem like things deteriorated very quickly over the last couple of days. It was a shame. He's an amazing man.
"I watched and read a lot about him. Even over the last day or so I went on the BBC Sport web page and the first 11 stories were all on him and all different things.
"Some were him speaking to kids, some were him the way that he talked before his fights, and some were stories of other boxers who fought against him or had met him and what he meant to them.
"He was clearly just an amazing man. He was actually the one person I had always said I would love to meet him.
"I don't meet loads of famous people, but he's one famous person I would have loved to meet. I'm sad about that, as well."