We measure the internal attenuation of bulk crystals of chemical vapor deposition zinc selenide (CVD-ZnS), chemical vapor deposition zinc sulfide (CVD-ZnSe), Si, and GaAs in the short near-infrared (sNIR) region to evaluate the possibility of astronomical immersion gratings with those high refractive index materials. We confirm that multispectral grade CVD-ZnS and CVD-ZnSe are best suited for the immersion gratings, with the smallest internal attenuation of αatt=0.01 to 0.03 cm-1 among the major candidates. The measured attenuation is roughly in proportion to λ-2, suggesting it is dominated by bulk scattering due to the polycrystalline grains rather than by absorption. The total transmittance in the immersion grating is estimated to be at least >80%, even for the spectral resolution of R=300,000. Two potential problems, the scattered light by the bulk material and the degradation of the spectral resolution due to the gradient illumination in the diffracted beam, are investigated and found to be negligible for usual astronomical applications. Since the remaining problem, the difficulty of cutting grooves on CVD-ZnS and CVD-ZnSe, has recently been overcome by the nanoprecision fly-cutting technique, ZnS and ZnSe immersion gratings for astronomy can be technically realized.