Midrasz do Kapłańska 22:8

3) I would know that only their meal-offerings (are permitted to Cohanim). Whence do I derive that their melikah (bird-offerings are also permitted to be eaten by Cohanim)? R. Shimon says: (If not apprised otherwise) I would read (Vayikra 22:8): "Neveilah (carcass [including, ostensibly, a melikah offering] or treifah (an organically "torn" animal) he (a Cohein) shall not eat to defile himself therewith" (If he does eat it, he is forbidden to eat kodshim). It is, therefore, written: "for Aaron and for his sons," to permit the melikah offerings of Israelites.

5) I might think that the neveilah of a beast confers tumah upon clothing (when it is) in the esophagus; it is, therefore, written (Vayikra 22:8) "A neveilah and a treifah he shall not eat to become unclean." (The allusion is to the neveilah of an animal [i.e., a bird],) which confers tumah only by being eaten — to exclude the neveilah of a beast, which confers tumah (even) before it is eaten.

6) I might then think that the neveilah of a bird confers tumah (in the esophagus) by Scriptural edict, and that of a beast, a fortiori (viz.: If the neveilah of a bird, which does not confer tumah by touch, does so by being eaten, how much more so, the neveilah of a beast, which does confer tumah by touch!) It is, therefore, written (Vayikra 22:8) ("to become unclean through it" [the neveilah of a bird]) — Only through it is tumah conferred upon clothing by being swallowed, and not through the neveilah of a beast.