The Parkhead captain is wanted by new Dons boss Stephen Glass in a player-coach role.
Brown would continue playing while also acting as Glass’ assistant.
Celtic have reportedly put forward a one-year extension but with no manager announced there is a degree of uncertainty for Brown remaining at Parkhead where he has played more than 600 games and won 22 trophies.
Glass and Brown formed a close relationship while at Hibs and the new Dons boss sees the midfielder is an influential figure, on and off the field, as part of his management team.
His appointment to replace Derek McInnes was confirmed on Tuesday and he has vowed to implement an “attacking style”.