To have no idea or no recollection; to have no lead or relevant memory about something.
財布をなくしたが、心当たりがない。
I lost my wallet, but I have no idea where it might be.
その人の名前に心当たりがないと答えた。
I answered that I had no recollection of that person's name.
警察に聞かれたが、心当たりがないので協力できなかった。
I was asked by the police, but I couldn't help because I had no idea.