The Celtic skipper, 27, has struggled with the complaint all season with manager Neil Lennon so far selecting him only for important European games. Brown missed Scotland's 2014 World Cup qualifying double-header against Serbia and Macedonia but it hoping to be available for the away games in Wales and Belgium next month.
However, he is first looking to return for the champions in Perth but failing that, he hopes to feature in the Hoops' opening Champions League clash against Benfica at Celtic Park next week. Lennon has mentioned the possibility of an operation for Brown but the midfielder said: "Hopefully not, we will see how it is for the next couple of weeks."
He added: "I have had two weeks off resting and I will see if I can play on Saturday, if not, next Wednesday. There is a bit of wear and tear and some inflammation as well so I have to sit out here and there in training.
"It all started at the end of last season when I got my hernia operation. It's just nipping here and there but it seems to be a lot better these days."
Brown gave a flippant response when asked to assess Celtic's chances of getting out of a Champions League group which also includes Barcelona and Spartak Moscow.
He said: "Easy. It should be a six-pointer against Barcelona as well. So it should be guaranteed I think."
The former Hibernian player admitted the Celtic squad have been buoyant since knocking Helsingborg out of the play-offs.
"It has been four years since I played in the Champions League and a lot of the lads came to Celtic expecting and hoping to play in the Champions League and now they are, everyone is looking forward to it," he said.
"It is a happier place, everyone is bouncing about and looking forward to the games. Benfica are going to be good on the ball but we need to try to win our home games, that's the first thing and see what we can get in the three away games."