Hamilton's future has been the biggest talking point in the Monza paddock building up to Sunday's Italian Grand Prix for which he will start from pole, the 23rd of his Formula One career.
Off track, though, the speculation surrounding Hamilton continues to dominate on the basis his management team, XIX Entertainment, are known to have spoken to Mercedes.
Although in "advanced negotiations" with McLaren, Mercedes are in the hunt for the 27-year-old should Michael Schumacher decide to retire for a second time.
Three-times Formula One world champion Stewart, however, believes Hamilton would be foolish to leave McLaren given the positives of staying with the Woking-based marque.
"I personally would stay with McLaren," said Stewart. "They have the resources, the money, the long-term commitment, huge experience.
"He wouldn't be here today without them, and there is a degree of loyalty which you should always have.
"McLaren haven't been out of the top-end of motor racing now for a very long time.
"You go to Mercedes, who are a wonderful company, it would take a five-minute decision from the board for them to decide to stop motor sport should there be a problem with the economy.
"So if I were thinking long term, then I would think to stay with McLaren. I can't imagine how you could be more spoiled than being with McLaren."
There is a train of thought that after 14 years with McLaren and the possibility he is growing stale, the lure of pastures new to reinvigorate Hamilton's career is tempting.
Stewart can appreciate the logic, but feels a bedding-in process would be required at Mercedes, especially as they do not have a winning car at present, taking the chequered flag just once in 50 grands prix.
"Going to a new team would probably take him 24 months to settle down, with new engineers, new management, new cultures, new ways of doing business," added Stewart.
"He might immediately dial the car in and get it done. Going to a new team might give him a regeneration if you like.
"If he is deep inside McLaren and he doesn't think they are going to do the job for him, then he should move.
"But if it's a borderline issue, then he should stay with the diet he knows best.
"Sometimes the devil you know is better than the devil you don't know."
Stewart also recognises Hamilton may not appreciate just how good his life is at McLaren, adding: "Probably not because he's been with them since his karting days.
"He's a very lucky boy because he's made huge amounts of money, and that's been largely down to McLaren, not Lewis, because they gave him the break, made him the driver he is.
"But money is only a tiny part of it. In making a certain amount of money you're not going to make a lot less whether you go to one team or the other.
"So it's nothing to do with money, but it's a very big decision in his career, and I think he'll stay with McLaren."