Can fibroadenoma turn into cancer?

Very Unlikely: Fibroadenomas are benign tumors of the breast. They are quite common and are not precancerous. Very rarely there have been cases reported where a fibroadenoma has been thought to turn into a tumor called a cystosarcoma phyllodes of the breast which is a very unusual type of breast cancer.

Benign but depends: Fibroadenoma of breast is a benign disease , rarely transforms to malignancy , but if there is a family history of breast cancer , chances increases to 3.7 , compared to normal population who did not have family history of breast cancer.