Brown has struggled with injuries in the past, but the Scotland international midfielder is now fully fit and is playing well.
The 31-year-old former Hibernian star has established himself as a key player in the current Celtic team.
Brown has praised Rodgers for the impact that he has made on his game since his arrival at Celtic Park.
The former Liverpool manager was appointed the Celtic manager in the summer following the departure of Ronny Deila at the end of the 2015-16 campaign.
SB: The manager has came in and changed my game a lot. He has taken me to a new level.— Celtic Football Club (@celticfc) December 12, 2016
SB: I'm learning different ways to play and I'm enjoying it.— Celtic Football Club (@celticfc) December 12, 2016
Celtic are at the top of the Scottish Premiership table at the moment with 40 points from 14 matches.
The Bhoys are eight points clear of second-placed and Old Firm rivals Rangers and have three games in hand.
The Glasgow giants will return to action on Tuesday evening when they take on Hamilton Academical at Celtic Park in the Scottish Premiership.Celtic will head into the match as favourites and should pick up all three points.