That's one of the warnings they rattle off on the commercial for Avodart (dutasteride), tenderness of the breast area. Both dutasteride and finasteride are the same 4-azasteroidal class of drug compounds, so they inhibit 5-AR through the same mechanism. Thus, both run the risk of this side effect.
I might ask what reason you are taking this to give me a better understanding of your concern. These drugs are prescribed for people with the assumption that their natural chemistry is overly favorable to DHT, thus causing side effects as hairloss or BPH.