The goal of this paper is to estimate the soft X-ray signature associated with dense and fast magnetosheath jets streaming toward the dayside magnetosphere. We developed a non-self-consistent kinematic approach for simulating numerically the transport of high-speed plasma jets in the magnetosheath. Our methodology is based on global magnetohydrodynamic simulations which provide the background state of the terrestrial magnetosphere and theoretical insight on the propagation of high-speed plasma jets. We compute line-of-sight and time-integrated intensity maps of the soft X-rays generated by the charge exchange process taking place when the high-speed jet interacts with the background exosphere. The X-rays are detected by a virtual telescope launched into the simulation domain. Our results show that the soft X-ray signature of a dense and fast plasma jet is visible in the magnetosheath. We can correctly characterize the detected jets with different setups for the virtual telescope. The impact of density on the jet's X-ray signature is stronger than the impact of bulk velocity, the denser jets being more likely to be detected by an X-ray telescope than the faster ones. We discuss an image processing technique based on frame differencing which may allow an improvement of the X-ray visibility of high-speed jets. We also show that the detection of jets is enhanced considerably when the soft X-ray telescope is placed in the equatorial plane, pointing toward the magnetotail.