Hamilton and Verstappen are locked in a tight battle for the world championship and, despite having overtaken each other at every race this season, they have managed to keep things clean so far.
But Brown thinks that the intensity of their rivalry makes it inevitable that at some point there will be a controversial coming together between them.
“I think rivalries are great for the sport and having those two guys go at it is good,” said Brown, speaking at the launch of McLaren’s Gulf livery for the Monaco Grand Prix.
“Hopefully, at some point over the course a year, that creates an opportunity for us, because I think it is just a matter of time until they both are determined to not let up in to Turn 1 and neither come out.”
Brown thinks that the head-to-head between Hamilton and Verstappen is a huge positive for F1, and has helped the sport see the best of both drivers.
“I think it’s great for F1,” said Brown. “Lewis has had a pretty easy ride out, apart from his one year with Nico [Rosberg].
“So I think it’s a great rivalry. I think Max has gotten Lewis to step up, not that he’s needed much stepping up. But he’s definitely on his A game.
“I think it’s clear that Lewis is a very smart driver. You can just see him sitting there waiting to strike and isn’t kind of over eager. I think that’s his experience coming through.”
McLaren driver Lando Norris says the close battles between Hamilton and Verstappen have been fun to watch – and offer an interesting view in to the different approaches from both drivers.
“Max goes for those opportunities, like Turn 1 [in Spain],” said Norris. “It was quite a risky thing.
“If Lewis had turned in, they would have crashed. So Max was pretty committed with his move. But they are the opportunities Max needs to take at this stage because they [Red Bull] are a bit slower.
“But it’s also what makes it fun, because then Lewis has to come back through and try to get past him. So it’s fun.”