The 28-year-old, who arrived at the DW Stadium in 2007, suffered a stress fracture last term which caused him to miss the last two games of the campaign.
Bramble was initially given a rehabilitation period of 14 weeks, which would have seen him sidelined right up until the opening weekend of the new season.
But the stopper is winning his race to fitness and could be available for Latics' first game of the season against Blackpool next month.
"The foot feels good," Bramble told the Observer.
"I've been in and out of the club over the summer and it's just a case of getting the strength back now.
"I think I'm doing as well as I could be at this stage, and fingers crossed it stays that way.
"The initial estimate was 14 weeks out, but I'm hoping that was worst-case scenario.
"I'm definitely aiming to beat that and I think I can."
Bramble says he is eager to get back on the pitch following a long summer out of action.
"It's been so frustrating because, although you're resting, you always like to do a little bit over the summer," he said.
"I just haven't been able to do that, not even joining in 5-a-sides with my mates. You can only really go on the bike in the gym, and that kind of rehab is so boring.
"But it's part of the game. I've had a few injuries down the years and I know the drill."
More urgency has been added to Bramble's fitness fight after Gary Caldwell was ruled out until October following surgery on both hips.
"There's more pressure on me to get back with Gaz out for a couple of months," he added.
"It's important we have as many guys available as possible for the gaffer to choose from.
"If you don't play well, you shouldn't take it for granted you're playing the next week."