But 1996 world champion Damon Hill thinks it could be time for him to move on.
Celebrating his 100th race at Hockenheim this weekend, 2008 world champion Hamilton is reportedly considering leaving the famous British team that gave him his Grand Prix debut back in 2007.
"I see no need for him to move away from McLaren," triple world champion Stewart told the Daily Mail. "I think it would be quite daft if he did.
"He knows they have got the resources," added the 73-year-old Scot. "You have to have the basic ingredients and McLaren have all of them and know how to do it and they have got a very experienced group of people."
Stewart also thinks Hamilton, 27, will find it hard to get "the sort of salary he enjoys" elsewhere.
"McLaren are a special team, a massive team and you do not give up a race seat there lightly," he wrote in his latest Telegraph column.
Coulthard said moving to Lotus would be a "huge punt" for Hamilton if he wants to win the world championship again.
"No, I would advise Lewis to stay right where he is, and I am sure he will," added the Scot.
But former Williams title winner Hill said Hamilton might be right to think the grass could be greener elsewhere.
"I'm sure Lewis feels that his trajectory had him down for at least two world championships by now, if not three," he told the Express newspaper.
But Hill conceded: "To try a move might be a risk for Lewis. But the counter argument is whether you can grow successfully within the same organisation.
"When you start off as a very young boy with an organisation, sometimes it's difficult for that organisation to realise that the young boy is no longer a young boy, he's a man, able to make his own decisions and go in his own direction.
"It can be a question of whether he gets that at McLaren."
Stewart, meanwhile, said he thinks Michael Schumacher should finally call his 19-season F1 career a day after his Mercedes contract expires this year.
"He should have got it out of his system by now in my mind," he said.
"I would like to see him maybe getting a victory this year and then retiring."
F1 chief executive Bernie Ecclestone disagrees, arguing that he is "always happy" to see the iconic German on the grid.
Former Force India driver Adrian Sutil agrees: "If I was in his situation, I would probably go on too," he said on German television Sky.
And Hans-Joachim Stuck, the German motor racing federation president, told Spox: "In my opinion, he is long overdue for a win."