Championship leader Piastri is 10 points ahead of second-placed Norris after five grands prix of the 2025 season having recorded three wins to his team-mate’s one.
Piastri and Norris – next in action at the Miami GP this weekend – are free to race, with McLaren having no designated No 1 driver.
There have been no major incidents between the pair as yet, although Brown expects that to change and is looking forward to getting a clash out of the way.
He said: “I think it’s definitely a matter of when, rather than if.
“You have two racing drivers, whether in the same team or different team, that are next to each other for 24 races, someone’s going to lock a brake…
“So I’m kind of looking forward to getting it over with because I don’t think it’s going to be anywhere near as exciting as everybody thinks.
“I think it will be a racing incident when that day comes. I think it’s inevitable.
“They’re two great characters. Neither of them are hotheads, so we’re not worried about it, and to a certain extent, kind of looking forward to just getting it out of the way.”
Brundle: Brown is preventing McLaren ‘meltdown’
Sky Sports F1’s Martin Brundle says Brown’s acceptance that there will be a Piastri-Norris collision means the team will not go into “meltdown” when it does happen.
“It’s incredibly smart what they are doing,” said Brundle.
“What Zak is saying there is that ‘papaya rules’ [McLaren’s way of saying ‘keep your racing clean’] will become ‘papaya wrecks’ at some point.
“[He’s saying] ‘we’ve got two incredibly fast drivers with a potential championship-winning car and it’s going to get rough at some point’.
“What that is doing is managing down so the team doesn’t go into meltdown, the drivers, the drivers’ entourages, and indeed the media.
“What he’s saying is ‘we know it’s going to happen, we’ll manage it when it does turn up, but don’t all overreact to it’.”