No Scottish team has gone through a full league season without defeat since 1899 but Brendan Rodgers’ side are within two games of doing so.
And while the Parkhead side have been coy in recent months about reaching the landmark, as it becomes tantalisingly close, Brown has admitted that it would be an incredible achievement.
"It would be unbelievable to do that,” he said.
"The lads were fantastic up at Aberdeen on Friday night and we now have two games to go.
"It is there to be done and we need to make sure we do it. We can't get sloppy or sit back and think it's done already.
"Partick are a good team. They will defend well and try to hit us with pace on the counter.
"It will be hard but we know if we turn up then on the day we can beat anyone.
"There is a focus to do that. It's an aim for us to stay unbeaten.
"When you go back to the first game in Gibraltar, the focus for us was to get better.
"We have done that, game on game, and we need to maintain that level now.
"We have set standards and the gaffer is huge on us sticking to them - in training and games.
"There is no hiding place on the pitch. Everything is monitored through GPS, heartrate monitors and pro-zone.
"We need to maintain our levels. The gaffer demands that and he wants us to play proper football.
"We have pace and players like Moussa Dembele, Scott Sinclair and Leigh Griffiths scoring goals. It's a good place to be right now but lose one game and everyone is on top of you - so we have to maintain those levels.”
Brown will be available for Celtic on Thursday evening after combining a two-game suspension with a family break. The player is expected to feature for Scotland against England on June 10th, and it is Gordon Strachan that Brown attributes to the maturity within his game now.
“I missed the run-in to us winning the league at Tannadice [in 2008],” he said. “I came back with two games to go and we had won four or five in a row, so I was on the bench for the last two games.
“I came on, but I thought to myself that I better change my ways instead of missing the games, and I wanted to be part of the team that won the league.
“Don’t get me wrong, it was phenomenal still to be part of the squad and winning games, but from there, Gordon sat down with me and we spoke about it and I went on to have one of my best seasons the next year.
“I felt as if I owed him. Everyone knew I was a wee bit immature when I signed, and it was more on the field than anything.
“Instead of following the man back I would end up trying to win the ball and mistiming the tackle, picking up silly bookings and that sort of thing.
“It was just about changing small parts of my game to improve everything and he was the one who done it, and that’s why I owe him.”