"Right now he would be the number one up-and-coming heavyweight in the world, in my opinion."
Smith also likes what he sees in Parker, and while understanding of his gradual progression through his undefeated 17 fight career (15 knockouts), believes the time is right to start pitting him against more evenly matched opponents.
"Parker's right in there but he's a few years younger. I think he's three years younger than even Joshua," he said.
"At 23, you take your time with him but step up the competition, fight different type of styles, but get some guys that have a little bit more speed and power and can actually hit him back.
"You have to step him up against a guy who has the ability to compete with him, and speed and size are what they need to match Joseph up (with).
"I'm sure that's what we'll see in the coming months with him. I'd be very excited about the prospects for Joseph Parker."
Parker's next fight is against experienced 31-year-old American southpaw Jason Bergman (25, 11, 2) at the Rumble in Paradise in Samoa on January 23.