The Canaries are understood to be trying to establish if Lennon would be interested in succeeding Chris Hughton, who was sacked on Sunday.
But, while the 42-year-old Ulsterman has never hidden his ambition to one day manage in the English Premier League, leaving what he describes as a "very stable club" to take over at a relegation-threatened outfit, would not appear to be his dream move.
Brown has himself resisted the lure of England because he gets such a kick out winning trophies and competing against the very best in the Champions League.
And he believes Lennon is bitten by the same bug.
Brown said: "I can understand why clubs are interested in him. He has done a great job here. What he does with us, day in and day out, is all about football and making it entertaining for the fans. He loves the club more than anyone here, that's for sure."
Brown continued: "His record is incredible. Everyone can say it's because Rangers are not in the top league, but I think the results would be the exact same even if they were there because he puts that drive and winning mentality into you. It's what he had as a player as well."
Brown does accept, however, that, if and when a job offer does land on Lennon's desk, he will have a big decision to make.
However, he has already declared that he wants to finish his career at Parkhead, and does not care if anyone considers that to betray any lack of ambition on his part.
"The main reason I want to stay here is the Champions League and winning trophies," he explained. "I don't want to go down the road and play in relegation battles.
"I want to win, week in week out, and this is the biggest club in Scotland by a mile and we're doing that."
Despite making it three-titles-in-a-row, Brown recognises it is Lennon's achievements in the Champions League which catch the eye of owners and chairmen outwith these borders.
And he is sure the lure of tilting at more windmills retains a massive pull on Lennon.
"He wants to go again in the Champions League," said Brown.
"I'm sure he'll be looking at players and what we can improve upon to get better and get back into the group stage."