Despite a one-off clash in the Italian Grand Prix, Norris and Piastri enjoyed a harmonious relationship in 2023, with Norris the de facto team leader in his fifth year with the Woking squad while Piastri came in as a rookie.
The scoreline reflected their different experience levels, with Norris scoring over double the number of points of the Australian as well as seven podiums compared to two.
Piastri did score a win in Qatar's sprint, something Norris has not yet managed.
But Piastri's impressive rookie season underlined his credentials as a star of the future and after Norris admitted the youngster was keeping him on his toes at McLaren, McLaren expects Piastri to only get stronger in the coming years.
With Norris and Piastri often closely matched on raw speed already, Brown says the team is prepared for the pair to look "after their own interests" but says he and team principal Stella will "get ahead" of any tensions.
"Not a concern, there's an awareness that anytime you have two drivers that one is going to have to beat the other at some weekends," Brown said.
"They're super competitive right now, you feel a real energy around them driving for the team. We know there will be a day, probably sooner rather than later, when they're looking after their own interests.
"I feel Andrea's and my strengths are around driver management, so I think we can get ahead of that and manage it to make sure it stays a healthy competitiveness."
Brown said the team had a "healthy conversation" when Norris and Piastri collided at the first chicane in Monza rather than letting any potential issues linger.
"We've all seen from our experience in Formula 1, you can see train crashes coming," he explained. "You don't know exactly what the team bosses do, but you kind of sit there and go: 'I'd be kind of getting on that now' and it strikes me from the outside looking in sometimes you've seen things escalate and it doesn't appear the team's jumped in soon enough.
"So after Monza, which is the first and only time they touched, we had a very healthy - there was no sweat - conversation, and don't wait till it happens a second time or third time.
"I think having once driven, not as fast as either of these two guys, I think helps understand the psychology of the driver and when and where and how to approach because I have seen you can approach drivers at the wrong time and you actually make it worse."
Additional reporting by Alex Kalinauckas
