A winger with blistering pace, the Best comparison was inevitable given that the two men were both from Northern Ireland.
However, looking back now, it is more Gillespie's attraction to a nasty vice than his footballing career that brings up memories of Best.
While drink was the demon that really ruined Best, gambling was the devil that saw the now 38-year-old Gillespie blow his fortune with nothing to show for it.
Gillespie's career never reached the height of Best's but spells with Newcastle, Blackburn, Leicester and Sheffield United in the Premier League did help him to earn more than £7 million in wages.
He lost some of that through bad investments but the bulk of it went straight to the bookmakers and he has warned that he won't be the last footballer to fall victim to the vice.
"You finish training and in the afternoon you go home and, if you’re not married, you’re probably going home to an empty house or a hotel room," he said.
"You’re bored and you’ve got time on your hands, and a lot of money to play with.
"In the old days, when you were physically going to a bookmaker’s shop, you could only lose what was in your pocket. Now, with internet accounts and telephone accounts, it is a lot easier to lose a lot more money a lot faster."
Gillespie said he once lost £47,000 on one afternoon's worth of bets of horse racing and then a further £22,000 the following day as he chased his losses.
Other footballers such as Dietmar Hamann, Matthew Etherington and Michael Chopra have opened up about their gambling addictions in the past but Gillespie says the majority of the people with the problem are probably battling the illness in private.
"There has been plenty of publicity about players with gambling problems but I guarantee you that there are a lot more out there who have not been named yet," he said.
"I am not the first footballer this has happened to and I won’t be the last.
"Gambling has become more and more prominent in the game. It has become more of an issue."
Gillespie says he still has an occasional bet but that he has it under control.
"It is not an issue for me anymore. I have three children now and I am aware of my responsibilities.
"I have probably grown up later in life than most people do but now I want to provide for my kids financially.
"If I thought it was going to be an issue for me again, I would seek help. But now if I have a bet, it’s usually on golf and it’s not very much. I don’t have very much.
"I regret the fact that I lost all that money but it’s the kind of character I am, always looking for a buzz.
"It was part of the life I led as a professional footballer and I wouldn’t change that. I lived out my dream."