Alliss, whose father played against Snead in the Ryder Cup in the 1930s and 40s, met with Snead several times, most recently when he was the honorary starter at this year's US Masters.
And he told BBC Sport Online of his sadness at the passing of a genuine golfing legend.
"He was the most beautiful golfer. I would say he could well be a candidate for the athlete of the century," he said.
"I don't think many could match his elegance and his longevity.
"If you think of someone like Sebastian Coe running, he had that elegance.
"Certain soccer players had it too, Bobby Charlton, George Best, Maradona - they moved with elegance and style.
"Sam Snead had all that, and he was an excellent golfer for decades. He had a wonderful poise and a beautiful walk."
Alliss said that Snead's amiable, easy-going style disguised a competitive man who was also a golfing innovator.
"He was so adaptable - he invented styles of putting that had never been done before," he said.
Naughty
"The nearest we have to him today is Retief Goosen, who is a similar sort of build.
"The way he hits the ball seems effortless, there is a lazy rhythm which is deceptive because it does fly. And that was very similar to Sam."
Alliss said Snead's achievements would guarantee him a place in golf's all-time hall of fame.
"He never won the US Open Championship and people will talk about that I suppose.
"But he was much more than just a good golfer. He had a rather naughty sense of humour," he said.
"With more and more great golfers emerging, it's getting harder and harder to make the list of 'all times greats'. But Sam would definitely be in my all-time top 10.
"He will be missed and it is another of the greats gone, which is tremendously sad."