Brown is on his way to Aberdeen to link up with his former team-mate Stephen Glass.
The 35-year-old will take on a player-coach role at Pittodrie.
The Hoops must now decide who will don the armband going forward after Brown, a 10-time SPFL champion and 12-time domestic cup winner, makes way.
27-year-old midfielder Callum McGregor is currently the vice-captain at Celtic Park, but some Celtic fans have a different option in mind.
However, Ajer may be a somewhat problematic selection.
He’s into the final year of his contract.
These Celtic fans back Ajer for captaincy
“Could Ajer not be the perfect fit ? Offering him a new contract and captaincy might be enough to tempt him to stay .. should be doing everything we can to keep him”
“They should give it to Ajer”
“To persuade Ajer of staying, I would give the captain band to him. He has all the right leadership skills from what I have seen over the last few seasons. We lose him, I will be gutted”
“If we could keep Ajer, he should be the captain. Why we do not have a manager in preparing for next season and sorting stuff like this out is madness. Failing to prepare is preparing to fail.”
“If Ajer remains at Celtic I think he’d be an excellent captain, he’s all the attributes needed. In fact he reminds me of a young Billy McNeill”
“Ajer is the perfect choice for me, shame we’ve mishandled his contract situation.”