The Earth’s magnetosheath and cusps emit soft X-rays due to the interaction between highly charged solar wind ions and exospheric hydrogen atoms. The LEXI and SMILE missions are scheduled to image the Earth’s dayside magnetosphere system in soft X-rays and thus to investigate global-scale magnetopause reconnection modes under varying solar wind conditions. The exospheric neutral hydrogen density distribution is an important consideration in the calculation of X-ray emissivities. The value of this density at the subsolar magnetopause is of particular interest for understanding X-ray emissions near this boundary, and is used as a comparison between competing models of hydrogen distribution. This paper estimates the exospheric density during solar minimum by using X-ray Multimirror Mission (XMM) astrophysics observations. We searched 11 years of XMM soft X-ray data and provided a list of 193 events with a possible detection of X-rays of magnetospheric origin. These events occurred during relatively constant solar wind and interplanetary magnetic field conditions. During these events the location of the magnetopause was measured in-situ by heliospheric missions. Thus the location of the solar wind ions responsible for the magnetospheric emission are well constrained by observation. We detected one particular event on 12-Nov-2008 and and estimated an exospheric density using the Open Geospace Global Circulation Model and a spherically symmetric exosphere model. The OpenGGCM magnetosheath parameters were used to disentangle 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 cm$^{-3}$ at 10 $R_E$ subsolar location.