The 20-year-old Conlan was watching on television when fellow Belfast man Barnes reacted to his 15-0 semi-final defeat to China's Zou Shiming in 2008 by raging: "They can keep their bronze medal, I don't care. It's for losers."
Conlan and Barnes are part of a six-strong Ireland boxing squad heading to the London Games, which also includes John Joe Nevin, Adam Nolan, Darren O'Neill and four-time women's world champion Katie Taylor.
"Four years ago I was sat at home watching Paddy go crazy on the TV, telling them they could stick their bronze medal," said Conlon.
"I watched Paddy doing brilliantly and I wanted to fight him and achieve the same things.
"I sparred with him a few months later and he gave me a good boxing lesson and I didn't want to fight him again. I don't think he liked me at the time because I was always saying I was going to beat him, but now we're more or less best mates."
Conlan, who grew up on the city's Falls Road, won two Irish senior titles but was a virtual after-thought in terms of Olympic contention until he booked his place by reaching the quarter-finals of the 2011 World Championships in Baku.
Beaten by a single point in the last eight by world and European silver medallist Andrew Selby, Conlan's fleet-footed displays unveiled him as a top prospect and gave him the belief that he belonged at the top level.
"The Selby fight gave me a lot of confidence," added Conlan.
"Selby is much more experienced than me so I know I'm up there with the best. I've believed since 2004 I would go to the Olympics and since 2008 getting to London has been my dream, and it has come true for me."
For his part, Barnes insists he has long since shrugged off that disappointment in Beijing, and is in good shape to become Ireland's first ever double Olympic boxing medallist despite a year of injuries and inconsistency.
The 25-year-old suffered a hand injury which forced him out of a defence of his European crown and then suffered a shock first round loss at the 2011 World Championships, before winning through in the final Olympic qualifier.
Barnes said: "I think any sporting man who fails at something is going to be annoyed with himself. But I know it was a good achievement and I'm very happy that I fulfilled a lifetime goal to get an Olympic medal and I hope to add to it with a gold in the next few weeks."
Barnes' dip in form in 2011 means he will go into the Games unseeded and facing the possibility of meeting the likes of world number one Shiming again in the first round.
He joked: "If I get a point this time I'll be happy. Seriously, I'd love to fight him again. The seedings don't mean a lot. I've been at the top for four years and I've beaten all these guys before."
Meanwhile, Ireland's head boxing coach Billy Walsh denied suggestions that Taylor's non-appearance at Tuesday's boxing press conference, as well as the official Ireland team announcement last week, related to the pressure of approaching her first Games.
Taylor issued a statement in which she said: "My training commitments are more demanding than ever and every session is crucial at this stage of preparation.
"For me it has been a lifelong ambition to represent my country in the Olympic Games, so I want to enjoy the privilege and take it all in. I am aware of the expectation that is on me, but nobody expects more of me than myself."
Walsh, who believes all of his six-strong team are capable of returning with medals, said: "This is the way Katie has managed it for a number of years. She shuts herself away from the pressure and she deals with it pretty well.
"Katie is the flagship of the women's sport and one of the main reasons it got into the Games. Other countries are chasing her and trying to find ways to beat her. Without improvement they would be catching up on her, but Katie continues to improve. She is only 26 and time is still on her side."