Speaking ahead of next weekend's final Old Firm derby of the season, which could see the Hoops crowned Scottish champions against arch-rivals Rangers, Brown has urged his manager to continue his impressive work at Celtic rather than jump ship.
"The gaffer has been unbelievable since he came in," he told Sky Sports News. "The way he wants to play and the way we set up, everything is so professional now.
"It's been fantastic for myself and everyone in that dressing room. We hope he stays, he is loving his time here and he has that seventh title to pick up as well.
"It is always special to win a title at Celtic Park, against Rangers as well to do it on that day it will be special for everyone. I am sure the fans will be loving it.
"I think it is 10 games we are undefeated against them but every game is different. We are looking forward to it. They are going to make it hard for us as they have done in the past but we believe when we turn up we can win and dominate the game."
Celtic remain on course for a clean sweep of domestic honours this term, having also won the treble in Rodgers's first campaign in Glasgow.