The sport is run by American chairman Chase Carey, representing commercial rights holders Liberty Media, whose future at the helm after 2020 is the subject of paddock speculation.
Carey has said nothing about stepping down, while Wolff has tried to distance himself from the chatter by saying he is not contemplating a move from a team chasing a sixth successive constructors' and drivers' title double.
Five times world champion Hamilton told reporters at last Sunday's French Grand Prix that those running the sport should be neutral. [nL4N23V33E]
"I've been a bit conflicted the last few days," he said at the Austrian Grand Prix on Thursday. "I made a comment but I don’t feel like I probably got out exactly what I was meaning.
"Over these past couple of days I was thinking to myself, you know, bringing someone in that doesn’t know much about Formula One is not necessarily the right decision.
"I think Toto could do a pretty special job."
The question of who runs the sport post 2020 is a sensitive issue to teams, who are working with the governing body and other stakeholders on major rule changes aimed at making the sport more equal and improving the racing.
Hamilton had alluded to the Ferrari past of Jean Todt, president of the governing FIA who previously ran the Italian team at a dominant period in their history, when he spoke on Sunday.
"I know Jean is level, but the fact is he’s been with the red team for so long, surely when he wakes up, if there’s a red T-shirt and a silver T-shirt, surely he goes for the red one," said the Briton.
"Just like when I get out of bed and see 44 (his racing number) or six (former team mate Nico Rosberg's). I will go for 44. Toto has been Mercedes through and through for such a long period of time.
"I think the best is someone from outside who is neutral, if that is possible," he had said.
(Reporting by Alan Baldwin in London; Editing by Ken Ferris)
