The 36-year-old midfielder had 14 trophy-laden years with the Glasgow club and was a popular captain of the Hoops until heading north to team up with his old Hibs colleague Glass earlier this year.
The Aberdeen manager has no worries about Brown - who is also his assistant - being affected by the emotional aspect of the occasion when he plays in front of the travelling Hoops support in this weekend's cinch Premiership clash between the teams in the Granite City.
Glass said: "Everybody knew this was coming when Scott agreed to come here. He's almost dealt with a touch of it already when he played for Celtic against us last season and he knew he was coming here.
"He's the type of character who it won't affect. He wants to win football matches. It'll also be a little opportunity for the Celtic fans to say 'hello' and 'goodbye' to him, I suppose, because they never had that opportunity last year.
"The overriding thing for us is that Scott's determined to win a game for us on Sunday, and I don't think that ever changes. That's why he is what he is.
"Anybody who knows Scott knows there's no mixed emotions when he pulls on a jersey for a match. This weekend I don't think you'll see any mixed emotions from Scott, and I don't think the Celtic fans and players would expect any different, just as we didn't expect any different when he played against us last year knowing he was coming to Aberdeen."
Aberdeen go into Sunday's match on the back of two points in eight games, but Glass is confident the situation will improve soon.
He said: "The mood's good. We're obviously aware of the situation, that we've not got the points recently that we should have and that we feel we deserved, and it's important we start getting them quickly.”