McGeady came through the ranks at Celtic before leaving to join the Russian side in 2010.
And Brown, whose side will reach the knockout stages if they can better Benfica's result against Barcelona, believes Celtic fans will remember and honour McGeady's time at the club.
"I think Aiden will get a good reception," said the Scotland midfielder.
"He did really well when he was here. He was a joy to play alongside and he was a fans' favourite as well so I am sure they will give him that good reception at the start.
"But once the game starts, we are there to win it and so is he. It will be heated, fast and an exciting game to watch.
"I think we all know Aiden is a huge danger. He is a very talented boy, he is going to be a threat.
"He is enjoyable to watch and creates all sorts of problems for the defence and midfield so he is going to be one to watch."
Brown added he had cancelled an operation on a hip problem which has plagued this season.
"I am feeling good. It seems to be improving," added the 27-year-old.
"I have trained five or six days and there is no pain. I got 65 minutes at the weekend (against Arbroath) so that has definitely helped. I am going to continue until I can't train and can't play any more."