US-based Jamie - whose family hail from Greenock - appeared on Iron Mike's bird-based TV show 'Taking on Tyson', in which the ex-champ reveals his love for doos.
Pigeon fancier Jamie, 35, first got to know the 44-year-old heavyweight through mutual friends in both the fight and flight games.
Jamie told the Tele: "It's been very exciting to meet Mike and get to know him.
"I was an amateur boxer myself, so I have seen Mike in the passing over the years just to say 'Hi' to.
"I trained in New York as an amateur and hung out in the gyms and stuff, so it wasn't unusual to see Mike around the place.
"He is an extremely humble guy, and genuinely one of the nicest people you could ever hope to meet - an extremely engaging person.
"We're not on the phone to each other every day, but we are definitely pals now."
Jamie - whose mum and dad, Jim and Elizabeth, are from Greenock - was born in Brooklyn but spent his summers on holiday in Inverclyde as a youngster.
And he still comes over regularly to visit his gran, Mary Muir, at her home in Nicolson Street.
The 'Taking on Tyson' programme producers found out about the link between Jamie and the famous former boxer and invited Jamie to take part in an episode where his Brooklyn team take on Tyson's New Jersey pigeon crew in a showdown bird race.
Jamie - who runs a specialist coffee company with his brothers Craig, 25, and Alan, 34 - said: "When we raced for the show we were put into teams.
"Tyson was a great boxing champion, but he didn't do too well with the pigeons because he's a novice when it comes to racing them.
"But he's kept pigeons since he was about 10 and the way he handles the birds is amazingly gentle and some comparison with what most people have seen of him in the ring.
"It is amazing how many people involved in boxing also have a passion for pigeons too - and Mike has a real affection for them.
"It really is some crossover between boxing and pigeons."
Jamie, who speaks with a distinct Scots-American lilt, said: "Mike is undeniably the most colourful heavyweight there's ever been, and he still has that aura about him - a real presence when he walks into a room."
"There is a real misconception about him.
"But at least I can say I took on Tyson and won."