Phelps's success has been announced at baseball games and even rock concerts and shown on big screens.
"Having Bruce Springsteen come out at a concert and say I'd just won my seventh gold medal and then sing 'Born in the USA' - it's incredible, you never realise it could happen - you're speechless."
When he was growing up, one of Phelps's heroes was basketball legend Michael Jordan, and he said he hoped he could follow in his footsteps.
"Growing up, I always remember the 'I want to be like Mike' ads with Jordan," he said.
"He's one of the people I've always wanted to meet. I've never met him.
"What he did in the sport of basketball is what I am trying to do in the sport of swimming. He completely changed the sport of basketball."
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