McLaren has emerged as Red Bull's closest challenger since the summer after bringing a raft of highly effective upgrades to its MCL60 since Austria.
Norris has taken five podiums across the past six races, with two for rookie team-mate Oscar Piastri, as McLaren is reaping the rewards of a technical restructure under team boss Andrea Stella.
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The consistency of its resurgence, which has set it apart from the more fluctuating form shown by Ferrari and Mercedes, has raised expectations the Woking squad could take the fight to Max Verstappen and Red Bull in 2024.
When asked if that's a realistic prospect, Norris replied: "Maybe. I've just been just saying to Max, since we bought this upgrade to Austria, I've been the second highest scoring driver on the grid. I think we've been the second highest scoring team, potentially.
"Of course, we've taken some massive steps forward and at the same time, considering we’re talking about fighting the Red Bull, I think it's still a very, very good thing what we've achieved this year.
"We're talking about one of the best drivers in Formula 1 ever, in one of the most dominating cars.
"And for us to go from where we were in Bahrain to getting close and talking about fighting a Red Bull, I think are very good signs for us. We know we still have plenty more things to come next year, so I'm excited.
"There’s no point thinking of it until next year but I'll be optimistic and I believe we can do it as a team."
Arguments in McLaren's favour include its new wind tunnel, which came on stream in July in time for the start of the 2024 car development, as well as other key facilities.
However most of its new hires, including Red Bull's Rob Marshall, will start too late to have an impact on its 2024 launch car.
The counterargument to McLaren's challenge is that Red Bull enjoys such a sizeable advantage in 2023 that it has been able to focus nearly all of its development resources on next year's car in contrast to its rivals.
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Stella believes that while McLaren's breakthrough across 2023 gives it a good starting point to attack next year, he cautioned the development curve that the teams have embarked on since the summer will play a more pivotal role than the Woking team's strong finish to the season.
"Where you are with next year's car partly depends on where you are this year, because that's the starting point for everyone," he said.
"But the gradient as development that you have for six, seven months is much more important. You have such a long period which is just about the work you do on next year's car.
"The work that we are currently doing in terms of aerodynamic, mechanical development is much more important than the starting point."
