The British driver finished second to the Australian at the Chinese Grand Prix on Sunday (23.03.25) and expects to have close internal battles with his colleague as the British team seemingly has the fastest car this season.
Norris said: "I think we're both excited - probably nervous and excited at the same time - as I'm sure the team will be.
"But we're ready. We know that as much as we work together and we have a good time and enjoy ourselves, we both know we want to try and beat each other and show who's best.
"And that's inevitable. So there's no point trying to hide away from that fact or make something of it."
Norris holds the early lead in the drivers' standings but stressed that he and Piastri must work together to press home McLaren's advantage over their rivals in the initial phase of the campaign.
The five-time race winner said: "I think we both achieved something better this weekend because of that [help].
"And we'll continue to do that.
"Like Oscar said, at any point other teams can find something... They can catch up quicker than you think, just like we did last year.
"We also have to think as a team and keep pushing the team forward from that side."
Norris admitted that he was "lucky" to finish the race in Shanghai after suffering a brake issue in the closing stages of the Grand Prix.
He said: "I was lucky. Lucky to finish the race today, which is not something you want to be saying.
"Brakes are something you hate but something you really do need and they can save your life. It's just the worst feeling when you go to press the brake and nothing happens and your foot just goes to the floor."