Could Hamilton take key engineers to a new team, like Schumacher did?
Schumacher took technical director Ross Brawn and designer Rory Byrne from Benetton to Ferrari, where he enjoyed his heyday surrounded by allies that he already knew.
Hamilton’s contract with Mercedes expires at the end of this year and, aged 38, he is yet to commit amid underperformance from the W14.
F1 pundit Herbert told the Evening Standard about Hamilton’s future: “I suppose it’s down to what happens at Mercedes.
“Can they turn it around? If that doesn’t work and Lewis still has the fire in his belly and thinks this is not the place for him where does he go?
“Would he go to Ferrari? Does he want to go there as he feels that’s where he gets a championship?
“Would he feel he could take his energy and people from Mercedes there like Michael Schumacher did and actually change and steer it in a positive way? The problem with that is time.”
Hamilton and Schumacher are joint-record holders for the most F1 championships, with seven.
Even if Max Verstappen romps to a third consecutive title this season, as looks likely, he remains a long way short of their tally.
“I don’t like driving not great cars,” Hamilton smiled to Fox Sports. “I don’t like driving a car that’s not the car that we weren’t meant to have but I love that challenge of ‘OK, what can I do with it?
“Wins are not possible right so what is the maximum we can get? “Can we be a little cheeky and if fifth is the best we can get, can we get a fourth or a third?
“Just make sure we are consistent and fit and ready so when the car does all of a sudden switch on and it is the car you dreamed of having, you’re ready.
“I am ready to win a world championship. I have prepared the best way I can this year - the best I have ever prepared - and if the car comes correct tomorrow I will be ready to fight for the world championship but unfortunately that's not the case.
“I am working with everyone here and back at the factory to get there.”