Lennon stepped down from his position as the Celtic manager at the end of last season following four successful years.
One of the most important players during those four years was Brown, who is the current Celtic captain.
The 29-year-old Scotland international midfielder established himself as one of the best players in Scotland, and Lennon has spoken highly of him.
“You talk about leadership and influence on the team, well I look at Steven Gerrard at Liverpool and I feel Broony’s the same kind of inspirational player for Celtic,” the former Northern Ireland international midfielder told The Sun.
“Gerrard sets the tone, sets the example for the rest of the Liverpool side — and Broony does the same.”
Gerrard is one of the greatest players in Liverpool history, while Brown is one of the best midfielders in the Scottish Premiership.
The players have won a number of major trophies with their respective clubs. While Gerrard has clinched the FA Cup and the Champions League among others, Brown has guided Celtic to Scottish Premiership, Scottish Cup and Scottish League Cup triumphs.
Former England international midfielder Gerrard will leave Liverpool at the end of the season.
Brown’s current contract with Celtic runs until June 2018, according to Transfermarkt.co.uk.