The WBO lightweight champion, 29, takes on Kevin Mitchell at Glasgow's SECC venue on Saturday night in what will be his 37th professional fight.
However, it was in his winning debut against Woody Greenaway at the city's Kelvin Hall in 2001 that he caught the eye of 'Marvellous' Marvin, the former undisputed world middleweight champion.
At ringside Hagler told Alex Morrison, now Burns' manager, that the boy from Coatbridge would one day be world champion.
Burns has reached the top of the mountain and is looking for his 20th straight win but is still self-effacing and at times "embarrassed" by the attention he receives - no matter when and where it comes from.
"That was actually my first fight at the Kelvin Hall, where Hagler was commentating," he said.
"It is unbelievable that someone like Marvin Hagler would say that but again, stuff like that doesn't really bother me.
"I just want to get in there and get on with my job. I don't really like all the attention and all the spotlight on me.
"All that side, I seem to get embarrassed by it all.
"People have asked me how I have changed since becoming world champion.
"I haven't changed as a person but my attitude towards boxing has.
"I am getting more confident. I am getting stronger and I can see a big improvement.
"Come fight night, it is always good to have your home support but once that first bell goes, I will put it to the back of my mind and get on with the job.
"I think it is going to be a great night."
The friendship between Burns and his Dagenham opponent has been well chronicled in the build-up to the keenly-awaited contest but the champion will not allow that relationship to affect his aims.
He said: "I have known Kevin for a few years, we came through the ranks together and have always been with the same promoter.
"But once you step into that ring it is down to business.
"It is my job. Once I am in there I will do what I need to win.
"I said hello at a conference call last week but there has not been much contact.
"We have a press conference on Thursday and we will speak then but most of the talking will be done in the ring.
"I am expecting a tough 12 rounds but we have prepared for what happens on the night and the fans are in for a treat.
"I would like to say a big thanks to everybody who is coming to SECC and who are watching on Box Nation at home and hopefully I can do the business."