Verstappen is caught in a McLaren sandwich at the top of the standings, 12 points behind Lando Norris and four ahead of Oscar Piastri.
Norris was asked on Thursday about circumstances possibly requiring the Australian to move over at the season-ending Abu Dhabi Grand Prix and said he would not be asking for that.
Brown told Sky Sports television, however, that McLaren would want Piastri to yield.
"Yes, of course. We're realistic," he said. "We want to win this drivers' championship.
"If we get into the race and it's becoming pretty clear that one has a chance and the other doesn't, we're going to do what we can to win the drivers' championship. It would be crazy not to.
"We're not going to not win the championship because we're trying to protect a third and a fourth, or a sixth and a seventh, or however the situation may play out."
Norris will be champion if he finishes in the top three whereas Piastri must win or finish second to stand a chance.
Brown said Formula 1 had always been a team sport and played down the risk of a backlash from fans.
McLaren have already secured the constructors' title for the second year in a row.
"If one of them can't win, they want the other to win," he said. "And that's what the team wants. And they are team players and we've already seen that last year.
"I don't think it's unusual in any sport for teammates to make sacrifices for each other to give the team what they want."