The McLaren racer secured his maiden world title at last weekend's season-ending Abu Dhabi Grand Prix and is keen to test himself against his illustrious compatriot next year as the seven-time champion looks to bounce back from a difficult debut campaign at Ferrari.
Norris told Sky Sports News: "I would love to race a bit more with Lewis.
"Obviously, Ferrari struggled a lot more this year than I think everyone was expecting.
"Lewis has proved himself to be probably the best of all time. Everyone knows if anyone can bounce back from difficult years, it's Mr. Hamilton, and I would love to race against him more."
The British driver added: "It's always a privilege that I get to race against someone that is the best in the world. You have got a good amount of those guys. You have Fernando (Alonso), Lewis, Max (Verstappen).
"There's a lot of us that want to climb in the footsteps of these guys. George (Russell) and Oscar (Piastri) are two of these and there's so many guys on the grid."
A major rules reset means that the 2026 season could be very different but Norris is ready for the challenge of defending the title.
He said: "Next year, everyone's got an opportunity. Everyone's looking forward to it.
"People want to come to take my crown, and I want to try to retain it. And I look forward to that battle."
However, Norris won't get much time off to savour his title success before another gruelling campaign begins.
The 11-time Grand Prix winner said: "Work starts even earlier next year than it normally does, by almost three weeks, so a much shorter holiday.
"Just get out somewhere, enjoy some time away with my friends and family.
"And by the time I go, 'This is nice', we're going to have to get back to training and get ready for next season, but I'm looking forward to some good days off that everyone deserves."