The size dependence of the magnetic phase transition in reentrant ferromagnet NiMn is investigated. Multilayer films of NiMn/Cu with thicknesses between 30 and 13 000 \AA{} are prepared using the ion-beam sputtering method in an ultrahigh vacuum. The ferromagnetic (FM)--reentrant-spin-glass (RSG) transition temperature ${T}_{\mathrm{RSG}}$ is determined based on the irreversibility in the temperature-dependent dc-susceptibility $\ensuremath{\chi}(T).$ The Curie temperature ${T}_{C}$ is assigned to an inflection point in the $\ensuremath{\chi}(T)$ curve. At thicknesses greater than 200 \AA{}, the transition temperatures are analyzed based on finite-size scaling, and the shift parameter \ensuremath{\lambda} and the characteristic length ${D}^{0},$ at which the magnetic phase transition disappears, are evaluated. For the FM-RSG transition, ${\ensuremath{\lambda}}_{\mathrm{RSG}}=0.66\ifmmode\pm\else\textpm\fi{}0.44$ and ${D}_{\mathrm{RSG}}^{0}\ensuremath{\sim}8\AA{}$ are obtained. For the paramagnetic (PM)-FM transition, ${\ensuremath{\lambda}}_{\mathrm{FM}}=1.31\ifmmode\pm\else\textpm\fi{}0.28$ and a remarkably large value of the characteristic length ${D}_{\mathrm{FM}}^{0},$ $43\ifmmode\pm\else\textpm\fi{}13\AA{},$ are evaluated. This large value of ${D}_{\mathrm{FM}}^{0}$ is discussed in connection with the inhomogeneous spin fluctuation appearing in the FM phase, which is found based on previous M\"ossbauer observation. The PM-FM and FM-RSG transition temperatures, as functions of thickness, intersect at a critical thickness ${D}_{c}$ at which the FM phase disappears. Below ${D}_{c},$ in addition, the spontaneous magnetization disappears in the low-temperature phase. This observation indicates that there is a vertical boundary line through the thickness of ${D}_{c},$ which separates the reentrant ferromagnet, having a low-temperature RSG phase with ferromagnetic correlation, from the pure spin glass. This is compared with the magnetic phase diagrams of reentrant ferromagnetic systems.