A third successive Old Firm victory on Sunday would see the Hoops secure the championship for a seventh consecutive season and extend their unbeaten run in the derby to 11 matches.
However, Celtic captain Brown has stressed that the most important thing is to "turn up, because anything can happen on the day".
"It'd be lovely to do it at Celtic Park in front of our own fans," the defender told Sky Sports News. "It means the world to them to see us getting a trophy, winning leagues and winning more titles, but the main thing is we need to make sure we do the business on the day.
"We believe we can win every game. We've got top-quality players, whether it's on the bench or the ones that are starting. We go into games and we believe, we've got confidence, we've got a top-quality manager that's behind us as well.
"You always want to win against Rangers, you always want to prove a point, especially in the city as well, but we need to make sure we turn up, because anything can happen on the day."
The last Old Firm derby saw Celtic run out 4-0 winners over Rangers in April's Scottish Cup semi-final at Hampden Park.