Dyer was stretchered off with a suspected broken ankle in Sunday's 1-1 draw with Norwich at Carrow Road, but scans show the winger has suffered no break, although a ruptured lateral ligament will keep him sidelined for an extended period.
Taylor broke and dislocated his ankle against Sunderland in September 2012 and missed most of the rest of the season.
"It's great to hear that Nathan's injury is not as bad as first feared, as bad as everyone thought," he told the South Wales Evening Post.
"Looking at it back, it could have been a lot worse, so we're thankful that it's not too bad."
Taylor returned from his injury at the end of last season and has appeared nine times for Swansea in all competitions - five of which have been in the Europa League - this season.
The Wales international is pleased to have avoided picking up any knocks since his comeback.
"I've worked really hard and the key for me was not to get any muscle injuries, which people often get when they come back," he added.
"I've been back since about February, I feel good and thankfully this season has kept everyone busy."