However, Brown has first revealed he wants to prolong his playing career as long as possible, before learning the managerial ropes elsewhere.
In the immediate future, a new contract at Celtic could be in the offing for the 'Hoops' captain as he looks to continue the successful run under Brendan Rogers.
"Myself, the gaffer and Peter (Lawwell) have been chatting and it seems to have gone well," he said of contract talks.
"I am just concentrating on playing right now. I'll go and do my badges in the summer but I'll see how long my legs last before I think about moving upstairs.
"It's a great honour to be playing at the club for so long and for them to be helping me out with a coaching role, whether it's under 16s or whatever. It's an exceptional place to get a start. I've learned a lot under the manager here and the previous managers.
"But I'm still playing so I've not thought about managing the club one day. You never know. The manager here now has set a great standard and I still have a lot to learn.
"I'm learning every day, from his sessions, the way he deals with situations, the media, public, everything. It's all first class. That's why he has the reputation of being a top manager."