It was narrated from 'Adiyy bin Hatim At-Tai that:

he asked the Messenger of Allah about hunting. He said: "If you release your dog and mention the name of Allah over him, and he kills (the game), but does not eat any of it, then eat. But if he has eaten form it, then do not eat, for he caught it for himself, and not for you."

أَخْبَرَنَا عَمْرُو بْنُ يَحْيَى بْنِ الْحَارِثِ، قَالَ حَدَّثَنَا أَحْمَدُ بْنُ أَبِي شُعَيْبٍ، قَالَ حَدَّثَنَا مُوسَى بْنُ أَعْيَنَ، عَنْ مَعْمَرٍ، عَنْ عَاصِمِ بْنِ سُلَيْمَانَ، عَنِ الشَّعْبِيِّ، عَنْ عَدِيِّ بْنِ حَاتِمٍ الطَّائِيِّ، أَنَّهُ سَأَلَ رَسُولَ اللَّهِ ﷺ عَنِ الصَّيْدِ قَالَ " إِذَا أَرْسَلْتَ كَلْبَكَ فَذَكَرْتَ اسْمَ اللَّهِ عَلَيْهِ فَقَتَلَ وَلَمْ يَأْكُلْ فَكُلْ وَإِنْ أَكَلَ مِنْهُ فَلاَ تَأْكُلْ فَإِنَّمَا أَمْسَكَهُ عَلَيْهِ وَلَمْ يُمْسِكْ عَلَيْكَ " .