The Oxford United midfielder received treatment following a 50/50 challenge in the 1-0 win at home against Stoke City, and was substituted during first half stoppage time.
Brannagan came close to requiring surgery for a medial collateral ligament (MCL) injury, but instead has gone through a course of injections to avoid surgery and a significant lay-off.
The 28-year-old went for a check-up with a specialist this week, and the outcome was a positive one for the U’s ace.
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He told BBC Radio Oxford’s The Dub podcast: “I’m going along well with my prehab and I’m working my way to getting back on the pitch now.
“It was better news than I expected, so I was quite happy with the news that I did get.
“At first, I got told I was going for surgery, which was obviously frustrating and probably would’ve been looking at about five months that I would’ve been out for.
“I got some good news this week that all my injections that I did have went well, and now it’s just a case of building up to hopefully getting on the pitch sooner rather than later.”
There is no set timescale on when Brannagan will be back out on the pitch, but he is hoping for a return to training within four weeks.
He said: “The specialist did say ‘whenever your body is ready, you’ll be right’. It’ll just be a case of that to be honest.
“I’m hopefully trying to get on the pitch within four weeks, to try and train maybe, but that’s down to myself and my body, and how I feel.
“There’s no real time on it. It’s just when I’m ready to be honest.
“I’m itching to get back as you imagine. It’s killing me being in the physio room, but at the end of the day, I was probably a couple more strings in the MCL from having surgery.
“I got away with one and I was quite lucky. I’ve just got to make sure I come back right because the last thing I want is to do it again and be out for even longer. I need to make sure I’m right before I do anything.”
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On his absence from the field, Brannagan said: “It’s very tough. I’m passionate when I play and watch, and I’ve been watching the boys from afar on iFollow or at the games.
“The lads are doing really well, so it’s pleasing to see and the only downfall I would say to the lads is that we should’ve got more points from some of the games that we’ve played in.”
He added: “There are many worse things in life than an injury, and that’s the way I see it. I’m always quite positive about the situation.”