Ecclestone was reported at the weekend as saying that in mid-2012 Hamilton had asked for his help to get a contract at Red Bull.
Those efforts failed to come to fruition, however, with Red Bull owner Dietrich Mateschitz preferring to remain loyal to Mark Webber.
Hamilton said he was aware of Ecclestone's comments, but he was confused as they did not tally with his version of events.
"He seems to only make comments about me for some reason," said Hamilton when asked for his feelings on Ecclestone's remarks. It makes me a bit nervous because we have quite a good relationship and I'm quite open with him about a lot of stuff.
"I don't really know what to say about the comments he made.
"I think he said something about me talking to Red Bull? I said to my management team to speak to all the teams and give me what the best options were.
"There was no particular one that I was pushing for more.
"At the end of the day I am here [Mercedes] and it's the best decision I have ever made."
Hamilton took his first podium for Mercedes in the Malaysian Grand Prix on Sunday.