On the eve of the new season, Christian Horner has now told British reporters that - with Hamilton's current contract expiring this year - it is "difficult to envisage Lewis in our team".
Hamilton, the 2008 world champion who had a tumultuous 2011 and was famously beaten by Button in the drivers' points standings, insists he doesn't mind.
"It's the first time I've heard of (the remarks) but they definitely don't wind me up," the Briton is quoted by the BBC.
"There are a lot of opinions, and everybody has their right to an opinion, but it doesn't really affect me.
"It doesn't really matter at the end of the day when I go out and do the job."
In fairness to Hamilton, he sounds confident and refreshed heading into the new season, has patched up his relationship with his girlfriend, and appointed Didier Coton to look after him in the paddock.
"Lewis was a child prodigy -- this is the problem," 1996 world champion Damon Hill told the Sun. "When you have been brought up from an early age to be a product, at some point something will crack."
"I don't think Lewis will ever be out of demand for the top teams," said the Scot.
Lewis was a child prodigy -- this is the problem
"What are Lewis' other options? I don't think Mercedes are waving around a cheque book -- I'd be surprised if Michael (Schumacher) and Nico Rosberg are in the top-four earners in Formula One.
"You also want a competitive car and if McLaren give him that, then he will probably stay," said Coulthard.