A surge in competitiveness by McLaren since a mid-season upgrade has left the Woking-based squad just 49 points behind Aston Martin in the fight for fourth place in the constructors' championship.
Norris has no doubts that McLaren now has a car that can help close the gap in the remaining six races, and thinks that an ace up its sleeve is the fact that he and team-mate Oscar Piastri are both delivering points.
This situation is in contrast to Aston Martin, which has lost pace in recent races, and seen driver Lance Stroll not score any points since the summer break. It means that in the last four races, his outfit has added just 25 points to its tally, compared to McLaren's 69.
Asked if he believed McLaren could now beat Aston Martin, Norris said: "Yes. I didn't think it was that close. But yeah, if it's 49, then I definitely think so.
"There's not many races left. I'm sure there's going to be a couple where Aston are going to be a bit stronger, but I think our advantage at the minute comparing to almost every team, bar a couple, is we have two drivers who are up there fighting for these positions and fighting for these points.
"Not every team has that at the minute, so I think that's helping us. We can help one another, we can use one another, and I think that's a good advantage we have over a lot of other teams at the minute."
Norris is coming off the back of two second places in recent races, having finished behind Carlos Sainz in Singapore and then following home Max Verstappen in Japan.
While McLaren is still chasing improvements to its MCL60, especially in low-speed corners, Norris thinks the overall package can now maintain good form for the remainder of the campaign.
"We're on an upward trend," he said. "We're making good progress and days like [Japan] prove exactly that.
"Even though I know there's going to be maybe some tougher races coming up at times, and maybe not as straightforward as [Japan], the progress we've made this season has been pretty incredible from my eyes.
"From where we were, to finishing 19 seconds behind the lead is I think evidence of exactly that. So I'm proud of everyone and we'll keep pushing."
But while Norris has set sights on beating Aston Martin, McLaren team principal Andrea Stella is playing the prospects down as he doesn't think there is any benefit to be had from getting focused on a set target.
"I don't even want to think that there's anybody at McLaren that needs this kind of carrot to push any harder," he said.
"I trust - and not only I trust - I believe, that everyone is pushing at the fastest reasonable sustainable pace. So that's what I want and that's what I think is happening.
"If we start thinking about, 'now we need to finish fourth, we can finish fourth', everyone would say, 'Andrea, we know already. You don't have to tell us. We don't have to declare this to the world.' We're just going as fast as we can. And that's the attitude."
Aston Martin is well aware of the threat that is now emerging from McLaren, as it battles to rediscover the form that helped it earlier in the campaign to a run of podium finishes.
Team principal Mike Krack said there was no doubt that the Silverstone-based team had to unlock more pace from the AMR23.
"It's a hard fight," he said. "I think we need to look at the upcoming races. We need to deliver the maximum in terms of reliability, which we have not done [in Japan]. We had one car at the finish, so we have to have no mistakes in the operations and focus on ourselves. We can not influence what they are doing.
"But there are some sprints. I think we will have some rain, probably. So it's going to be long and hard. I'm always confident, but we need to be better in terms of reliability and we need to add performance."
