Lennon was linked with Norwich long before Chris Hughton lost his job on Sunday as the Canaries battle to stay in the Barclays Premier League.
Another former Celtic player, Malky Mackay, is odds-on to replace Hughton on a permanent basis after youth-team coach Neil Adams was installed for the final five matches of the 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 Scotland 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 being 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."
And he hopes Lennon is also persuaded to stay by the opportunity to play in Europe's premier tournament and re-live moments like their comeback victory over Shakhtar Karagandy, which sealed their place in this season's group stages.
"It's been tough qualifying," Brown said. "We were 2-0 down and Jamesy (Forrest) scored in the last five or six seconds of the game, so it shows you how hard it is getting into the Champions League, and it shows what a good team we have when we are consistently doing it.
"It's the main reason people come to this club and it's why I'm still at this club. I enjoy fighting for the Champions League to get that occasion, to see 60,000 fans out there singing during the Champions League song."
Lennon himself expects to be considered for the role but he was diplomatic when asked about the vacancy during an appearance as a pundit on BBC's Match of the Day 2 on Sunday night.
"I'll be amongst a list of candidates, I'm sure," he said.
"I think the Premier League is one of the best leagues in the world but I don't want to be talking about that. I'm in a very stable situation at Celtic.
"People always think that the Scottish environment is obviously not as good as the English environment. But I'm at at a great club and it's a privilege to be their manager."
Celtic announced they had maintained last year's reduced season ticket prices and Brown is adamant that 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."