If Celtic were to defeat their Old Firm rivals on Sunday, they would secure the Scottish Premiership title for the seventh season in a row.
Brown said: ''It'd be lovely to do it at Celtic Park in front of our own fans. 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 the confidence, we've got a top-quality manager that's behind us as well.''
He added: ''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.''
When discussing the potential for a record breaking 'double-treble' this season, Brown was wary of Celtic maintaining their form and not getting swept up in the hype.
He said: ''That'd be incredible but we can't get too carried away with ourselves. We've got a huge game coming up on Sunday [against Rangers], we need to make sure that we win that first.''