The Earth's magnetosheath and cusps emit soft X‐rays due to the charge exchange between highly charged solar wind ions and exospheric hydrogen atoms. The Lunar Environment Heliospheric X‐ray Imager and Solar wind Magnetosphere Ionosphere Link Explorer missions are scheduled to image the Earth's dayside magnetosphere system in soft X‐rays to investigate global‐scale magnetopause reconnection modes under varying solar wind conditions. The exospheric neutral hydrogen density distribution, especially the value of this density at the subsolar magnetopause is of particular interest for understanding X‐ray emissions near this boundary. This paper estimates the exospheric density during solar minimum using the X‐ray Multimirror Mission (XMM) astrophysics observatory. We selected an event on 12 November 2008 from the XMM data archive, which detects soft X‐rays of magnetosheath origin while solar wind and interplanetary magnetic field conditions are relatively constant. During the event the location of the magnetopause was measured in situ by the THEMIS mission, thus the location of the solar wind ions responsible for the magnetosheath emission is well constrained by observation. We estimated the exospheric density using the Open Geospace Global Circulation Model (OpenGGCM) and a spherically symmetric exosphere model. The ratio of the magnetosheath plasma flux between the OpenGGCM model and the THEMIS, was nearly 1, which means the magnetohydrodynamic model reasonably reproduces the magnetosheath plasma conditions. The OpenGGCM magnetosheath parameters were used to deconvolve soft X‐rays of exospheric origin from the XMM signal. The lower‐limit of the exospheric density of this solar minimum event is 36.8 ± 11.7 cm−3 at 10 RE subsolar location. Key Points From 11 years of X‐ray Multimirror Mission‐Newton X‐ray observations, we identified 193 intervals that can be used to estimate the exospheric neutral density We derived a solar minimum exospheric neutral density from the 12 November 2008 event using a global MagnetoHydroDynamics model and a simplified exosphere model The density estimate is 36.8 cm−3 near the subsolar magnetopause and is likely a lower‐limit value