Genesis 1:11, 21, 24-25, 28-29 (ESV), 11 “And God said, ‘Let the earth sprout vegetation, plants yielding seed, and fruit trees bearing fruit in which is their seed, each according to its kind, on the earth.’ … 21 So God created the great sea creatures and every living creature that moves, with which the waters swarm, according to their kinds, and every winged bird according to its kind. And God saw that it was good. … 24 And God said, ‘Let the earth bring forth living creatures according to their kinds–livestock and creeping things and beasts of the earth according to their kinds.’ … 25 And God made the beasts of the earth according to their kinds and the livestock according to their kinds, and everything that creeps on the ground according to its kind. And God saw that it was good. … 28 And God blessed them. And God said to them (Adam and Eve), ‘Be fruitful and multiply and fill the earth and subdue it, and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth.’ 29 And God said, ‘Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food.’”
In Genesis, God designed all living organisms (plants and animals) to reproduce according to their “kind.” The Bible does not define the word “kind” in a classification system. However, organisms can be interbred and reproduce according to their “kind” if they are biologically related through a common ancestor. God seems to approve of interbreeding within kinds. How do we know?
Wheat was not in the Garden of Eden. Man selectively interbred primitive wheat to promote specific traits and to make wheat useful for food. Jesus gave us the Parable of the Wheat and the Tares. Wheat symbolizes true Christians.
Dogs were not in Eden. Man again selectively interbred canines to create large numbers of dog breeds. The unique dog breeds can successfully reproduce dogs according to their kinds.
However, when a horse and a donkey breed, the resulting offspring, the mule, is sterile. Thus, God has put a natural limit on what traits mankind may select for. But, this is not genetic engineering.
Since the Bible does not directly address your question, let us reason on the topic. The increase of knowledge (Daniel 12:4) brought people information about genes and genetic engineering. This can create problems. When genes are changed, we do not know all the unintended impacts the changes will have on the living plant or animal. Genetic codes which scientists once thought were unimportant seem to have distinct purposes. We believe mankind does not yet have enough knowledge to tinker with God’s design on the genetic level.