The Hoops boss is again being linked with a move to Norwich City, more so now than ever before following the sacking of Chris Hughton, but midfielder Brown is keen for him to stay in charge at Parkhead.
"He has done a great job here, it showed last year in the Champions League as well and winning the league, and this year winning the league yet again, and getting into the Champions League again was huge," said Brown.
"What he does with us on the field day in, day out is all about football and making it entertaining for the fans. He loves the club more than anyone at the club.
"Everything is a difficult decision, especially at a club this big, but we hope he stays and it would be great for the club if he stays."
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