This is what I thought at first:
You need a restoring force in order to have a phonon: after all, phonons result from the quantization of the lattice energy written as a sum of harmonic oscillators. The hamiltonian of a gas cannot be written in this way: there are no restoring forces (you cannot "pull" a gas), so there can be no phonons.
As Rococo wrote, quoting Xiao-Gang Wen, a sound wave (SW for short) in a gas is different from a SW in a solid. If you think about it, a SW in a gas cannot be thought of as an "excitation" above some "fundamental vibrational state": it is just energy transiting through the medium.
This is why you cannot quantize a sound wave in a gas, and hence you cannot introduce phonons in its description.
Then I talked with my professor of physics of liquids, and it seems like the subject is a bit more complicated than what I thought. He said that you can have collective excitations, hence phonons, in liquids, but there are some things to consider.
First, while the structure of a solid remains unchanged when a SW passes through it, this is not true for a liquid: the liquid can "restructure" itself locally with a certain speed. So, if the perturbation's frequency is greater than the inverse of the time it takes for the system to restructure itself, we will have a coherent wave. But if the frequency is smaller, the liquid will restructure faster than the propagation of the wave and the wave will undergo decoherence. The time it takes for the liquid to restructure can be estimated from the time it takes for the dynamic structure factor $S(\vec k, t)$ to go to $0$ (see figure below)
Another thing is that the wave vector $\vec k$ could be a bad quantum number to describe this kind of collective motion, since the liquid has no periodic long-range order and it is difficult to define for example a Brillouin zone. We can talk of normal modes of vibration, but we cannot apply the same formalism we use on crystals. This is also true for glasses and other amorphous solids.
I think many of these insights can be applied to gases too. The situation there is of course even more different from a crystal because short-range order (which is present in liquids) is lacking, too. So we can have collective motion only at very low $\vec k$, i.e. on large scales where the medium can be seen as a continuum.