The Hoops captain told BBC Scotland that he would jump at the chance to take charge of the club he has served as a player for more than a decade.
Brown, who turns 34 over the summer, has already spent time working with Celtic’s development squad and admits he won’t be resting much when he eventually does hang up his boots.
“I’m not one to just sit about and chill, enjoy life playing golf,” he told the BBC. “I’m going to go into coaching.”
When asked if that included the top job at Celtic, Brown said: “Everyone would love this job: every fan, every manager - especially in Scotland.”
Brown is on track to guide Celtic to an historic double treble, with a Scottish Cup final against Motherwell standing between the Hoops and a trio of trophies for the second successive year.
While he has declared he wants to keep on playing for a number of years, Brown has already started preparing for life after he calls time on his career.
“I had the chance to go and help coach the Under-20s with Stevie Frail and Tommy McIntyre - and I jumped at the opportunity,” Brown said.
“I was doing my B Licence so it was a great way for me to help push through that. I really loved it but it was just too much hard work doing thta as well as coaching during the day.
“Going to games at night, training during the day and then trying to focus on games on Saturdays and Sundays - I think the balance was just too much for me.”
The arrival of Brendan Rodgers, and his work with the champions, has had a positive effect on Brown, who has hailed the Northern Irishman’s impact at Parkhead.
“We got a top quality manager that almost won the Premier League with Liverpool,” Brown said. “He wanted to come here, which shows you the pull [Celtic] has.
“I’ve seen a lot of managers come here and leave with grey hair. I’ve also seen managers love the job and I think Brendan is the perfect one for that.
“He seems to be thriving, coming up to Glasgow and just enjoying life and management. It’s that love for the club and the desire to want it to do well - and I’ve got that,” Brown finished.