Earlier at Suzuka, amid rumours Brawn could step away from the Brackley based team, the 2008 world champion said he would “like him to stay”, as Brawn was “very influential in bringing me to the team”.
But Brawn, currently team boss, said he only wants to stay in “a role I’m motivated by and want to do”.
“We all want to get the situation clear as to how we are going to go into next year,” he told the BBC.
Hamilton, whose next boss is likely to be Paddy Lowe, has now said he supports Brawn’s decision and would also be happy under a new regime.
“He knows I’m a big supporter of his,” he is quoted by the Mirror, “but at the end of the day he has to do what it right for him.
“I don’t think it (Brawn’s departure) would derail my season next year,” Hamilton added.