Hamilton is contracted to the Silver Arrows until the end of 2020, although it is unlikely that McLaren will close the gap to the top three in that time, despite the strong progress being made in 2019.
Hamilton is Britain's most successful F1 driver, and has only Michael Schumacher ahead of him in many statistical fields.
Norris hopes he has a chance to test himself against one of F1's all-time greats while they remain on the grid together.
"That's something I would like, to be able to fight against Lewis," Norris told Sky Sports News. "A five-time world champion, possibly six this year.
"But it's a good two years before we're having a chance to fight them.
Hamilton and Norris both appeared at the pre-race press conference before the British Grand Prix, which Hamilton won.
The former McLaren driver spoke with delight at seeing how the team is doing so far in 2019, guided by the 19-year-old Norris and Carlos Sainz.
"It's amazing to see McLaren doing so well," Hamilton said. "They've had some really tough years as well.
"We got to have a bit of a race in the last race and just watching Lando's progression is incredibly impressive, to be so young in such an early phase, he's coming in and keeping a level head and delivering on weekends, also up against a driver who's got more experience than him."
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