Alain Prost is the former driver in question, the four-times world champion whose tactical acumen on the track earned him the nickname "The Professor".
Prost's smooth driving style was another hallmark of his character during grands prix, with many observers often comparing Button, and the way he caresses a car around circuits, to the Frenchman.
So when Button found himself being interviewed by Prost in Monaco recently for a French magazine, it is no wonder it felt "surreal" to the Briton who has admitted to modelling the way he drives on his idol. "It was quite uncomfortable, but it was nice," said Button ahead of this weekend's Canadian Grand Prix. "I've watched a lot of his races on TV, but you never really know what's going on inside a guy's head, so it was good to spend time with him.
"I was able to get his opinion on his racing as well as mine, and he was actually quite outspoken about me, which was good to hear."
Although Button declined to elaborate on Prost's comments, it is understood the 56-year-old was highly complimentary, leaving the McLaren star red faced and proud. But then given Button grew up watching Prost, more so than Ayrton Senna at a time when the two men dominated F1 and were obviously bitter rivals at McLaren, it is no wonder the comparison exists.
"It was good to understand the way he drives, the reason for his smooth style and why he didn't crash that often," added Button. "It all came from karting and the fact he didn't have a lot of money when he was racing, that he didn't want to damage anything because it cost money. He carried that style through, that he never wanted to hit a wall, never wanted to crash.
"He said that sometimes hurt him in his career, but most of the time it was a positive. He was also quite outspoken on his team-mates, that no-one had ever collected more points than him in fair races.
"For me, he is an amazing driver, and I still think he is bloody good. His ice racing shows he is still very talented. So for people to compare me to him is amazing because he is...I don't know if hero is the right word. But when I was growing up, when I was eight years old and started racing in karts, I was watching Formula 1 at that time.
"I suppose the reason why I drive like I do is because of the way he was."
For all intents and purposes, Hamilton and Button are a modern-day Senna and Prost, their respective styles mirroring those of the men they grew up watching, and to some degree, copying.
The one difference, mercifully for McLaren these days, is that the team's two current drivers are friendly towards one another, whereas Senna and Prost loathed each other.
"Nobody knows what it would be like if they were racing in Formula 1 now, but when they were racing they were outstanding and nobody could touch them," said Button. "For both of them to have a team-mate like the other was tricky, and they both had to be mentally strong.
"They were very different characters, but equally they could do a great job on the circuit, which showed. After all they were both world champions with the team. But for me I really liked the way Alain drove, and the way he used to think about his racing. We're all passionate about racing, that's why we do it, but he was a real thinker, and that means a lot."
Ahead of this weekend's race around the Circuit Gilles Villeneuve, where Button finished second to Hamilton last year, the suggestion is McLaren are favourites for victory.
However, Button said: "Qualifying will be tricky, although I think we'll be a lot closer to the Red Bulls, if not as quick as them.
"But you have to look at what Ferrari and Mercedes have with their DRS (drag reduction system), with the latter able to get more speed compared to the rest of us, which is a massive difference here.
"I would say they are our biggest competitors, which will come as a surprise to most people."