But he's being modest. "I don't always come across too well in interviews, then I'll read something that I've said and think, `They've changed it to make it sound much cooler than I ever could.'"
McConaughey is trying to convince me he's a lousy interview. He's holed up at the bar of the Four Seasons Hotel on a wet Saturday afternoon, drinking beer, sporting jeans, a battered sweater, and day-old stubble, and dutifully pumping quarters into the publicity machine for his new film, Amistad, directed by Steven Spielberg.
He seems, for someone with an aversion to interviews, completely at ease. Confidence, as you might expect from somebody who's been compared to Paul Newman in both looks and acting ability, is not lacking as he reflects on his tumultuous journey through Hollywood, from also-ran to overnight sensation, and, finally, bona fide movie star.
"I'm going through my golden period right now and the sun's shining brightly in my face. It's important, though, not to be blinded. You shouldn't lose sight of who you are. The higher up the ladder you go, the further you fall.
"I just try to do the work on a daily basis and hit it pure," he continues, alluding to his great love of golf. "Wherever the ball lies, you've got to hit it. It's about precision. It's about the gut. It's about the head. It's very internal - but at the same time you can get aggressive."
Since he exploded into the limelight barely 18 months ago, McConaughey, 27, has charted a careful course to build a career rather than be remembered as what he calls a "one-role wonder." Instead of chasing the money in big action movies like The Jackal, which he turned down, he has focused on quality material, fighting to play Jodie Foster's romantic interest in Contact; cutting his salary by $5m to work for Steven Spielberg.
Many in Hollywood are hailing McConaughey as the next Newman, but closer scrutiny reveals he possesses the brute elegance of another Fifties rebel to which so many young actors aspire, yet, sadly, only parody. Long-waisted, wistfully masculine, he's got the charisma of an early Marlon Brando.
"I think he's much more like Brando," agrees A Time to Kill director Joel Schumacher, who was responsible for giving him his breakthrough role. "But I do think he's a total original. I don't know anyone like him. There's an innate integrity and, yes, elegance about Matthew, yet there's a kind of shitkicking, dangerous side to him, too."
He will have ample opportunity to show that side in the future, but he's currently cropping up in roles that aren't as obviously his cup of tea. A case in point is Amistad, which, as McConaughey puts it, is "a big, big movie". Directed by America's premier film director, it features an international cast; a superb troupe of actors including Anthony Hopkins, Morgan Freeman and newcomer Djimon Hounsou. Spielberg had been considering many actors - John Cusack, Aidan Quinn, and Gabriel Byrne among them - for the role of Roger Baldwin, a New England property attorney who defends the mutinous African slaves aboard the Amistad, but he kept coming back to McConaughey.
Indeed, he was so determined to have McConaughey onboard that he paid $200,000 to another studio for costs incurred by the delay of taking him off another project.
The role of Baldwin was a first for McConaughey in that he played a real- life hero from history. Instead of researching the role to the hilt, like Daniel Day-Lewis or Ralph Fiennes might do, the actor insists he did not go through any elaborate measures to prepare for the part.
"I didn't read much about him specifically. This was the case he won and this is the story of how he tried it. I learned about it along the way.
"One of the tricks of me playing a character from 150 years ago is getting past hindsight," he explains.
"We all know, now, what Baldwin finds out at the end of the story; that slavery is wrong. But there's 150 years of ignorance to go back in order to play this guy in this time."
McConaughey, a southerner, says it was not difficult to maintain the slant that a New England lawyer might have towards blacks in the 1830s. "I tried to get into Baldwin's head, but keep my heart," he admits. "This is a man with no compassion. He's completely insensitive, almost callous to these men. He didn't see them as men. He saw them as property for the entire first-half of the story. He was about the case and not the cause. He knew how to win the case. He was oblivious to the rest. That was kind of cool." Fame, inevitably has brought him to the attention of the tabloids. He has been linked with Sandra Bullock, his co-star from A Time to Kill, but claims they are "just friends". Is he a womaniser? "I'm single, I'm young, I'm allowed. As you get older, that image isn't as cute, not like when you're 18 and going out with a different girl every week. When you're 40 and you do it, that's pretty sad."
"The truth of the matter is that I'm afraid that out of laziness I could end up letting a moment pass me by that could actually put me in a better position," he explains. "So I just keep working."