Both Britons are former world champions, but it was 2009 title winner Button who finished higher in his last's points standings -- a rare inter-team defeat for 27-year-old Hamilton.
But Hamilton insists he has made efforts over the winter period to remedy the personal problems that saw his 2011 season drive off the rails.
And the Daily Telegraph said he is not worried about the Button threat.
...my performances were pretty good.
"No, I don't have any concerns with it," he insisted.
"Considering last year, from my own personal feeling, that I wasn't performing at my best and I was still ... when you look at the qualifying positions - what was it, 13-6? - my performances were pretty good," said Hamilton.
He said he was able to usually out-qualify Button even though "a lot of (the) time ... my mind was elsewhere".
Meanwhile, Button, 32, revealed that he had dinner with Hamilton at the end of last season for only the second time in their more than two years as teammates.
"We had some steak and it was fun," he told the Guardian.
"The only other time we have dined together was when I signed the contract. It was good," added Button.