Taylor suffered the injury in his side's 2-2 draw with Sunderland last month and is expected to be out for the remainder of the season.
However, Taylor is happy with his recovery so far and is hopeful that he will be able to start jogging again in six weeks' time.
"I'm at the six-week stage today, and now I'm out of the cast and wearing a boot. I'm at the stage where I'm looking to get rid of the crutches over the next week or two and get walking normally with the boot on," Taylor told the club's official website.
"The six weeks seems to have gone fast, even though the first two weeks didn't seem like that at all. It feels like I have got somewhere, and I am told I am quite far ahead of where I should be, which is pleasing.
"Whenever you break a bone they say it is usually 12 weeks before you get strong enough to start jogging and things like that. At the end of the next six weeks I want to be able to jog. If I'm jogging by 12 weeks it will almost be a miracle the surgeons will say."
Taylor featured heavily in Swansea's successful season last year, playing in 36 of their 38 league games.