The Scotland international has been used sparingly by manager Neil Lennon this term, but he is expected to start Wednesday's UEFA Champions League clash with Barcelona at Parkhead.
Emilio Izaguirre, Thomas Rogne, James Forrest are all sidelined by injury, while Gary Hooper and Georgios Samaras are doubtful for the visit of the Spanish giants.
But Brown said: "I am starting to feel a lot better. I have had a lot of rest and my body is slowly getting better and better.
"I have managed to play three games in a row and I am feeling the benefits.
"So hopefully I am over the worst of it. You can never tell what is around the corner but my body is feeling good just now and if I can keep training day in, day out, playing two or three games a week, I am happy with that."
Lennon added: "It is perfect timing. The fact that he is recovering better gives us encouragement.
"He is playing at the top of his game, I feel, and he will be very important as he always is to us and in particular tomorrow evening, with his experience and drive a huge asset."