The full-back has been struggling with a thigh problem in recent weeks, but is now fit again and is in contention to make his return at St Andrew's.
Taylor suffered severe bruising and swelling to the muscle during Swansea's UEFA Europa League play-off first-leg win over Petrolul Ploiesti.
He has since been out for a month, meaning he has made just two appearances for Michael Laudrup's side this season.
However, the Wales international hopes to put his problems behind him and get back into the first-team - starting at Birmingham.
"It has been a bit frustrating being sidelined, but I’ve managed to come back ahead slightly of what we expected," Taylor told the club's official website.
"I’m looking forward to getting back into the squad and getting some game-time. Hopefully I can do that against Birmingham.
"The results have been excellent in the time I’ve been sidelined. We have been lucky that it has been just myself and Pablo (Hernandez) out injured, but I’m back now and Pablo isn’t too far away."
Taylor went on to stress the importance of Swansea doing their best to retain their League Cup crown, even though they are in the Europa League.
"We know what it’s like to lift a trophy, and we want to experience that again," he added.
"We have a squad of 22 here and anyone can play in any competition, which is great for the manager.
"It’s a chance to impress for whoever is selected and, more importantly, ensure that we progress to the next round."
‘If I was Bournemouth, I’d be thinking if they can get past Manchester City, there’s no-one to stop them winning the FA Cup for the first time ever’ Former England star believes the Cherries have the ability to make history
‘I wasn’t concerned I’d done anything wrong – I stated a fact. It was taken out of proportion and people have recognised that they misread the situation a bit’ Gary Lineker gives FourFourTwo his thoughts on BBC suspension for asylum seeker tweet
