كتاب الأشربة
36  
The Book of Drinks
(18)
Chapter: It is recommended to lick one's fingers and wipe the bowl, and to eat a piece of food that is dropped after removing any dirt on it. It is disliked to wipe one's hand before licking it, because of the possibility that the blessing of the food may be in that remaining part. The Sunnah is to eat with three fingers
(18)
باب اسْتِحْبَابِ لَعْقِ الأَصَابِعِ وَالْقَصْعَةِ وَأَكْلِ اللُّقْمَةِ السَّاقِطَةِ بَعْدَ مَسْحِ مَا يُصِيبُهَا مِنْ أَذًى وَكَرَاهَةِ مَسْحِ الْيَدِ قَبْلَ لَعْقِهَا
Sahih Muslim 2033 b

Jabir reported Allah's Messenger (ﷺ) as saying:

When any one of you drops a mouthful he should pick it up and remove any of the filth on it, and then eat it, and should not leave it for the Satan, and should not wipe his hand with towel until he has licked his fingers, for he does not know in what portion of the food the blessing lies.
حَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ، حَدَّثَنَا أَبِي، حَدَّثَنَا سُفْيَانُ، عَنْ أَبِي الزُّبَيْرِ، عَنْ جَابِرٍ، قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏ "‏ إِذَا وَقَعَتْ لُقْمَةُ أَحَدِكُمْ فَلْيَأْخُذْهَا فَلْيُمِطْ مَا كَانَ بِهَا مِنْ أَذًى وَلْيَأْكُلْهَا وَلاَ يَدَعْهَا لِلشَّيْطَانِ وَلاَ يَمْسَحْ يَدَهُ بِالْمِنْدِيلِ حَتَّى يَلْعَقَ أَصَابِعَهُ فَإِنَّهُ لاَ يَدْرِي فِي أَىِّ طَعَامِهِ الْبَرَكَةُ ‏"‏ ‏.‏
Reference : Sahih Muslim 2033b
In-book reference : Book 36, Hadith 175
USC-MSA web (English) reference : Book 23, Hadith 5044
  (deprecated numbering scheme)