Brown, 32, has not played a competitive game for the Black Cats since January, having numerous setbacks along the way.
The former Manchester United stopper had flown to South East Asia for a pre-season tour after it appeared he had regained full fitness, however his injury returned and has seen him sidelined since.
Having only made seven appearances for manager Martin O'Neill, the manager is looking forward to having the experienced defender return.
"Wes is making good progress, although the number of times I've said that is unbelievable," said O'Neill.
"He's not that far away again from getting back into training.
"He's had a few setbacks, but he's working exceptionally hard.
"It's been a frustrating time for him and it must get you down when you're out for that length of time."
Fellow centre-back John O'Shea is also currently sidelined, however his recovery looks far brighter, with the manager hoping to see him return within the next two weeks.
"He's responding well at this minute, quite well," added O'Neill.
"We were worried about it, but he is getting better by the day."