Brewster hasn't featured since an U23 game against Manchester City in January, having undergone surgery to repair ligament damage in both his knee and ankle.
Despite the problems, the starlet was handed his first professional contract by the club in the summer and has now stepped up his recovery after being spotted running at Liverpool's Melwood training complex last week.
When asked about the rehab, Brewster said it was going: “Really well. I've started to progress on the running side of things. I haven't had any setbacks at the moment and touch wood it stays the same because I can't wait to get back and try to get on the bench or maybe feature in a game.
“Hopefully, when I'm back, I will get a few opportunities and I'll take them, but I'm very happy with what I'm doing at the moment so hopefully the injury doesn't flare up again.
“Even if it does set me back a little bit I've just got to keep going. I will be back soon.”
With a December return pencilled in, Brewster will have been out for almost an entire calendar year by the time he is available again, but he feels his injury woes have helped him learn more about himself as an individual.
“You need to be mentally on point,” he explained. “With my injuries – especially being out for as long as I have been – I've gone through quite a lot: setbacks, things going through my head.
“To be fair, though, I think I've done exceptionally well for myself. People have told me that I have because, to be honest, I didn't think that I would be where I am now eight-and-a-half months ago.
“I thought I would've lost my head by now, but I've been mentally strong. You've just got to work hard and keep going and I think I have."
Meanwhile, Brewster also had words of praise for Liverpool boss Jurgen Klopp, thanking him keeping in touch during his recovery.
“The manager makes a few jokes about me not having been on the pitch for so long!” Brewster told Liverpool's official programme.
“But it's good to have a manager like that managing me because it does keep me happy.
“It would be easier for him to ignore me, think 'I'll wait until Rhian gets fit' and not really interact with me, but he has.
“He's kept my morale high and I can't thank him enough... well I could if I score some goals for him!
“Seriously, I can't thank the manager enough and also every single one of the players. They all talk to me every day, ask me how I am, when I'll be back fit and stuff like that. It means a lot.
“I just can't wait to be back and hopefully help the team go far in the Premier League and Champions League.”