The speed of light decreases with increase in the density of the optical medium whereas the speed of sound increases with increase in the density of the medium. So is there any possibility to construct a material where sound travels faster than Light.
It isn't possible to construct a material where the speed of sound is greater than the speed of light in a vacuum, i.e. $c$. That's because the interatomic forces that propagate the vibrations that make up the sound can themselves only propagate at the speed of light. Having said this you can get surprisingly close - in a neutron star the speed of sound can get pretty close to the speed of light.
But I'm guessing that you are specifically interested in comparing the speed of sound to the speed of light in the material, not the speed of light in a vacuum. In this case you need to appreciate that light propagating through a dielectric in not light. The interaction of the light with the dielectric causes the wavefunction of the light to mix with the wavefunction of the electrons in the dielectric to produce a quasiparticle called a polariton. So your question is really can the speed of sound be greater than the speed of a polariton?
And in principle the answer is yes it can. I don't know of any hard data comparing the speed of sound and light, but light can be brought to a complete halt in a Bose-Einstein condensate. Assuming these systems can propagate sound waves (which seems likely) this means that the speed of sound must be greater than the speed of light.
But be cautious about attaching any great physical significance to this. Remember that we are really comparing the speed of sound to the speed of polaritons, and there isn't any special significance to the speed that polaritons propagate.
I read an article about a group of scientist that where able to slow down the speed of light to around 40 mph, by producing a monochromatic light source then directing this light source through a dense arrangement of extremely cold Sodium atoms. I would suggest looking up a Bose-Einstein condensate, which is a condition when matter is cooled to near absolute zero. So there is conditions in which light can be slower than the speed of sound but i'm not certain about through that same medium.