The Briton, who claimed his maiden Formula 1 victory at the Miami Grand Prix three weeks ago, is 60 points adrift of championship leader and friend Max Verstappen of Red Bull after seven rounds of this year’s 24-race season.
"I’m 60 points behind Max and there is a long way to go," he told reporters ahead of this weekend's Monaco Grand Prix, avoiding suggestions that he was poised to mount a title challenge.
"So, I am definitely not thinking about it and it doesn't change anything.
"We've not thought about it over the last four weeks."
In the past month, since McLaren introduced a successful upgrades package, Norris has beaten Verstappen once and finished behind him in second place by just 0.725 seconds at last Sunday's Emilia Romagna Grand Prix.
"You just concentrate on getting a good result and things just play out for themselves," he added.
"But we've definitely put ourselves in it (teams’ title fight). We lost a lot over the first few weekends and that hurt us.
"But now it’s still kind of just a third of the way into the season so there are plenty of opportunities for us.
"We know some things are coming in the future and if things turn around we can easily come back again at some point."
Norris stressed that McLaren's car development efficiency and the teamwork of the two drivers – he and Oscar Piastri have both enjoyed strong performances in recent races – signalled they were making progress.
"Along with Ferrari, I think we're probably the team that has two cars up there performing in every single session, every single qualifying and the race," he explained.
"If you look at a lot of the grid, they don't really have that. You have one guy who has put in a mega lap and has a good race and then the other one not so much.
"One of our strings is that we've always had two cars up there and we can fight well along with Ferrari at the minute so if we keep doing that, then yeah, for sure we can stay in it."
By contrast to McLaren, Red Bull's second driver Sergio Perez has delivered inconsistent performances and last weekend at Imola qualified 11th and finished eighth in the race behind both drivers from McLaren, Ferrari and Mercedes.
