With the British team locked in negotiations over a new contract with 2008 world champion Hamilton, boss Martin Whitmarsh reportedly said the duo are a good pairing because they "learn" from each other.
"I don't know why Martin would say that, as I couldn't say what I have learned from Jenson," Hamilton is quoted by El Pais newspaper.
"I learned from Fernando (Alonso in 2007), but I don't particularly feel I have learned from Jenson."
The comments could indicate a growing rift between the McLaren teammates, after Button scolded Hamilton recently over the 'Twittergate' secrets affair.
And the awkwardness might also be powered by the fact that Paul di Resta, the Force India driver, has split with Hamilton's father Anthony and is now managed by a management partnership that involves Button.
On the Twitter affair, Hamilton commented: "I didn't mean to go against my teammate or my team, I just wanted my fans to understand.
"Now I know why I shouldn't (have done it) and it won't happen again."
"Well, no, I have no need or desire to be in a team like that; I like to be somewhere where I have to fight with my teammate," he said.
But he admitted he is thinking of going somewhere else.
"It would be nice to end where I began," said Hamilton, "but when your contract expires, you look around to see what else there is; if there are other challenges or opportunities.
"It's good for you to do that."
Triple world champion and legend Sir Jackie Stewart, however, urged Hamilton to stick with McLaren.
"(If) You go to Mercedes, who are a wonderful company, it would take a five minute decision from the board for them to decide to stop motor sport," he warned.