Norris finished sixth in the 2021 Drivers' Championship standings but has been tipped by many to fare better when the 2022 Formula 1® season begins with Sunday's Bahrain Grand Prix.
Norris watched on as Verstappen beat Mercedes' Lewis Hamilton to the drivers' title in contentious circumstances last year, attracting criticism from some quarters for what has been perceived as an aggressive driving style.
Speaking ahead of this weekend's curtain-raiser in Bahrain, the 22-year-old said he was not sure how he would deal with a rival as combative as Verstappen.
"It's a different battle, because of how Max races," Norris said.
"It's a different breed of drivers. You saw how he drove and changed when it came down to those final races, with aggression.
"It's maybe something you don't experience so much in the midfield because you're not going for a world championship, or some of the drivers don't have that mentality of risking everything.
"You would try and play smart as much as you can [when facing a rival like Verstappen].
"But I'm also a fair racer and, I don't know, maybe don't push the limits quite as much in certain areas."
Both Norris and new Mercedes driver George Russell are aiming to become the first British driver other than Lewis Hamilton to win a race for almost a decade, with Jenson Button the last to do so when winning the Brazilian Grand Prix in November 2012.
Meanwhile, McLaren are just seven podium finishes away from reaching a total of 500 in Formula 1®, with Norris recording four such finishes across the 2021 campaign.
Norris also claimed that Red Bull are pre-season favourites, as they look to end Mercedes' eight-year stranglehold on the constructors' championship, but highlighted Ferrari's credentials as potential contenders.
"I would go with Red Bull at the minute," Norris said. "But Ferrari are definitely the closest after that. They are downplaying themselves massively, as they would.
"But consistently, in every single run they've done, since the first lap [of pre-season testing] in Barcelona, they've been basically at the top.
"It was just the final day [of testing last weekend], when Red Bull brought some new parts along, they took a little step forward."
Norris has been tipped in some quarters as a potential title contender ahead of his fourth season in Formula 1®, and the 22-year-old says he is looking forward to the campaign and hopes to improve on 2021's showing.
"I'm confident. I'm ready for some good battles," Norris added. "I'm excited for what is to come this year.
"I am motivated to do better than last year. That's the aim and time will tell whether that's true or not.
"You ask most drivers 'will you ever be satisfied?' and I think most would say no. It is similar with all top athletes in different sports. They always believe there is a place [where] they can do better."