The Northern Irishman is believed to be close to signing a new deal with the Hoops and midfielder Brown is hoping he stays at Celtic Park for the foreseeable future to help the club achieve more success.
"The manager signing a new deal would be a boost for everybody," said Brown.
"Our relationship has definitely changed since we played against each other. Back then it was a hate-hate relationship between us.
"He's great to work under. He wants us to get the ball down. I'm not saying we're Barca but he wants to get as close to that philosophy as possible.
"He joined in the training game the other day and still wants to play. He passes on everything he did in his career and helps us in every way."