Hot, log (T/K) ∼ 7.5, gas was recently discovered in the Milky Way in extragalactic sightlines. In order to determine its location, here we present sightlines to Galactic X-ray binaries (XRBs) passing through the Interstellar Medium (ISM). In this pilot study we investigate absorption features of SXVI, SiXIV, and NeX in the spectra of three XRBs, namely 4U 1735-44, 4U 1820-30, and Cyg X-2, using Chandra High Energy Transmission Grating archival observations. We do not detect any of these lines. We determine the 2σ upper limit for the equivalent widths of the undetected absorption lines and the column densities of the corresponding ions. We note that the 2σ upper limits for SXVI Kα and SiXIV Kα are an order of magnitude smaller than those previously detected in the extragalactic sightlines. Our finding suggests that if any gas at log (T/K) >7 is present in the Galactic ISM, it is unlikely to be ubiquitous. This is an important result because it implies that SXVI, SiXIV and NeX absorption detected in extragalactic sightlines is not from the ISM, but is likely from a hot gas phase in the extraplanar region beyond the ISM or in the extended CGM.