We report the finding of a 1T phase island of NbSe2 on a cleaved surface and its magnetic properties. Tunneling spectroscopy at 400 mK shows robust peaks in the superconducting gap, which we assign to the Yu-Shiba-Rusinov (YSR) state originating from the magnetic moment placed in the superconducting state. The YSR peak appears on a specific position of an island of the 1T phase, not on the surrounding 2H phase area, and shows an anisotropic decay behavior. In addition, we found a close relationship between the enhancement of the YSR peak and the local curvature of the film. We assign the origin of the magnetic moment to the curvature of the 1T phase island, which can form a magnetic moment through a rotation of the wave function by a robust spin-orbit coupling, as indicated by a recent theoretical study.