The animals fit to serve as offerings are domesticated farm animals, not wild animals. The reason for this is in order to spare a person the exertion involved in trapping an animal to bring as an offering.

“An ox, or a sheep, or a goat, when it is born…it shall be accepted as a fire offering to the Lord” (Leviticus 22:27). Rabbi Yehuda bar Rabbi Shimon said that the Holy One, blessed be He, said: I have provided you with ten animal species of kosher animals. Three are under your control and seven are not under your control. Three are under your control: “An ox, a sheep, and a goat” (Deuteronomy 14:4), and seven are not under your control: “A deer, and a gazelle, and a fallow deer, and a wild goat, and an oryx, and an aurochs, and a wild sheep” (Deuteronomy 14:5). I did not make matters difficult for you by telling you to exhaust yourselves in the mountains to bring offerings before Me from the animals that are not under your control, but rather from the animals that are under your control – those that feed from your trough. That is the meaning of what is written: “An ox, or a sheep, or a goat” (Leviticus 22:27). (Vayikra Rabba 27)