Hamilton became Britain's most successful Formula One driver after clinching his fourth title in Mexico on Sunday.
Bookmakers William Hill have Hamilton as 15/8 favourite for the 2018 drivers championship, with Ferrari's Sebastian Vettel at 3/1 and Red Bull's Max Verstappen at 10/3.
Verstappen won Sunday's race, the third triumph of the 20-year-old's career.
Formula One has driver knights in Stirling Moss, generally regarded as the greatest never to win a championship, and triple world champion Jackie Stewart. Team principal Frank Williams and co-founder Patrick Head also have the honour.
Hamilton has the MBE, a lower rung of the multi-tiered British awards system, and went to Buckingham Palace to receive it from the Queen.
When asked about the chances of a knighthood, the 32-year-old winner of 62 races said he had always wanted to go back to the palace.
"That would be the greatest honour, to firstly be invited back," he said. "I try to represent England in the best way I can. If that at some stage is recognised by the Queen then I'd be incredibly honoured."
Hamilton wrapped the British flag around him as he celebrated on Sunday and has made much of his journey against the odds from an under-privileged background in the commuter town of Stevenage, north of London.
His paternal grandfather was an immigrant from the Caribbean island of Grenada.
"I wonder what the people who were at my school are thinking. There's a couple of teachers who said you're never going to amount to anything so I wonder what they're thinking now," he had mused on Sunday.
"I wonder if they're thinking 'I helped that young lad'. Or are they thinking 'you know what, I regret what I said. And I've grown from it'? I hope that's really the case."
Olympic athletics gold medallist Mo Farah and Wimbledon winner Andy Murray are also sporting Sirs but the Scot has emphasised he still wants to be called by his first name.
Hamilton joked he would be the opposite, if such a situation ever happened.
"I would enforce it. To everyone. To friends, everyone. I think it's such an honour," he laughed. "I've got friends who are Sirs and I call them Sir. When I get a text, I'm like 'Yes Sir.' It's unique and why not live it in all its beauty?."
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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