The 23-year-old had minor ankle surgery earlier in the week having struggled with ongoing problems towards the end of last season.
Now recovering, Brown believes he will return in time to help new boss Tony Mowbray and his team-mates achieve their European targets.
Quick to put to bed rumours that he may miss out in qualifying, Brown claims his operation was nothing more than a "clear-up."
"It seems some people want to do a bit of scaremongering but the medical staff are confident I'll be ready to play in the qualifiers," he told the Daily Record.
"I had the op on Monday night and although it feels pretty sore right now I've been told I'll be back training next week and I should be able to sprint again in a little less than four weeks from now.
"I'm a fit lad anyway so I see no reason why I should miss the start of the season," he added.
"It wasn't a major operation - it was just keyhole stuff, nothing more than a clear-up."
Brown confessed he needed painkilling injections to see him through Celtic's campaign last term.
"I was in a bit of pain at the end of the season and I needed injections to play the last few games.
"I suppose that hasn't really helped me in the long run because I've had to go under the knife.
"But I'm desperate to play my part in these qualifiers and to help the manager get off to the best possible start."