'I love racing, so there is no need to stop' - Hamilton
Referring to the 2008 world champion's soured relationship with McLaren as he considered a move to Mercedes last year, Ecclestone said: "Lewis told me that he would have rather taken a year off.
"In fairness to Lewis, he didn't leave McLaren over money," Ecclestone told business journalist Christian Sylt.
"I don't think I would leave this sport unless I didn't have a good feeling about it, or a smile and an energy when I got in the car. I love racing, so there is no need to stop.
"I am happy -- I think Bernie has a better memory than me," he is quoted by the Telegraph.
Given McLaren's early crisis in 2013, many now see Hamilton's move to Mercedes as inspired.
But although outwardly happy with his new challenge, team and 2013 car, Hamilton said he does not feel quite ready to win races or push for the title.
"I don't feel 100 per cent yet, and I think that showed in practice in Australia in the wet," he said.
As for the weekend's challenge at Sepang, the Briton admitted: "I don't think I am quick here.
"Fernando (Alonso) beat me on this circuit in 2007, in only my second Grand Prix, and since then I have not had a spectacular race here."