Another former Celtic player, Malky Mackay, is odds-on to replace the sacked Chris Hughton on a permanent basis after youth-team coach Neil Adams was installed as Canaries boss for the final five matches of the Premier League campaign.
But Lennon has never hidden his ambition to manage in England one day and his future was the main topic as Brown launched the club's season-ticket sales.
The Hoops midfielder said: "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.
"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."
Brown has himself been linked with moves south in the past but is happy staying with Celtic.
"The main thing is Champions League, winning trophies," the 28-year-old said. "I don't want to go down the road and play in relegation battles. I want to win week in, week out. This is the biggest club in Scotland by a mile and we're doing it.
"It's a great club and a great place to be, we have a good training ground and top-quality players as well."
Celtic announced they had maintained last year's reduced season-ticket prices and Brown is adamant they will offer value for money to supporters despite attendances appearing to fall as Celtic strolled towards a third consecutive title.
"We've got a lot more to offer," he said. "We have hopefully Champions League, we've got three qualifiers and they will be huge games.
"We'll have some new faces coming in and hopefully we will still have the same squad again. It's been entertaining this season and we are going to produce more."