To simply sum it up, why not? With the current acceleration of development of technology, we may very well be able to activate a series of microbots that physically alter our characteristics on command. That could be one solution, however, one must remember that this would be hard to "undo." If you see this question as "will we be able to morph back and forth from animals," or, "Will we be able to permanently change ourselves into animals." We will definitely be able to physically alter ourselves into the spitting images of some animals. Plastic surgery and tattoos along with many other methods could already do this today. So to the second question, yes, definitely.
However, to cover all my bases, I will focus on the first question; Morphing between the animal and human form(s). To morph between the animal form and the human form would be an impressive feat indeed. In order to do this, one could use mechanical plates to alter the face, and use chemicals embedded into the skin to change color, a few retractable wires and whiskers are born. This would probably take care of the face. The other physical characteristics of an animal could be harder to mirror. An ostriches long legs and plump body might be hard to copy. But also, a cheetah's increased muscle could prove to be a problem as well. We could go with today's solution, steroids. Temporary steroid use might theoretically alter the muscular system enough to pass it off as an animals. Many characteristics might require an undesirable solution, and some might be impossible to duplicate, but other than some extremes, most animal qualities could be copied. Regardless, with the rate of technological advancement will carve a path for physical altering, soon.
Many people might also want the question to say, "Alter our BIOLOGICAL qualities, or DNA, to almost match that of an animal." Now THAT will be hard. Due to the fact that all cells in the human body carry the exact same base plan of DNA, one would have to alter EVERY CELL in the body! That is an enormous task. Not even nanobots could accomplish that herculean feat, due to the constant reproduction of cells, it is just not reasonable. So the permanent ability to "morph" biologically from human to animal would be unrealistic. Notice, I said, "Permanent," The short term might be possible because the rate is fast, but we might be able to alter it for either a short period of time, or permanently until changed back. However, the process would almost definitely kill the subject. If the DNA is changed, all the cells will immediately start to alter, and I don't know about some people, but to me, that sounds VERY painful, if not lethal. But, for the sake of the argument, I will fall back on my standard, the technology doesn't exist, YET. It may very well develop in the coming years, and we may not even be able to fathom it. So to sum it up, Why not?