My consultants always told me it should feel soft. If it feels rock hard they can tell something might be off. This freaked me as i kept trying to feel it myself but they said it doesn't working doing it yourself!
That's funny because when my 1st transplant worked great the kidney felt ROCK hard. Then after 5 years it started to fail and it became softer and softer!
Now my 2nd transplant is working great and it's sort of inbetween, not TOO hard but not too soft. I think that's normal. I know that a transplanted kidney is NOT supposed to feel like a healthy liver, pancreas, stomach, intestines, etc.
During the transplant and with all the immunosuppression you get some scar tissue so it doesn't feel completely normal my nephrologist.