As Briton Hamilton and McLaren supremo Ron Dennis step up their war of words amid negotiations for a new contract, speculation the 2008 world champion could jump ship to a rival team - perhaps Mercedes or Lotus - continues to swirl.
"I'd like to see him stay," teammate Button, who is already under contract for 2013, said in Hungary.
"I'd love someone really slow as a teammate, but this place is like home to Lewis, he has been here since the start of his career.
"It's a massive change to go somewhere else," said Button. "I've done it a couple of times. Sometimes it's good for you.
"It's up to Lewis obviously but it doesn't seem, to me, like it would be the right thing to do."
McLaren chairman Dennis this week sounded unlikely to meet all of Hamilton's new contract demands, insisting "It's a question of whether we employ him, not the other way around".
But 1996 world champion Damon Hill had a word of caution for McLaren.
"His (Hamilton's) value is just going to keep going up and up if he carries on driving like that," the Sky pundit said after Hamilton netted a dominant pole at the Hungaroring.
Allan McNish, a former Toyota driver, described it as "one of the best qualifying performances I've seen".
Button, however, sensed Dennis might be serious.
"Maybe it's best to ask Lewis, he is the one with the choice to leave or not -- well, I don't know, I heard Ron Dennis say some interesting comments this week," said the 2009 world champion.