The stability of Néel skyrmions in ultrathin circular magnetic nanodots is calculated by considering the Dzyaloshinskii–Moriya exchange interaction (DMI) as an interface term. The areas of the single-Néel skyrmion stability/metastability/instability and skyrmion radius are determined as functions of the uniaxial out-of-plane magnetic anisotropy and DMI strength. It is shown that the well-known criterion of skyrmion stability in infinite film should be changed to describe the stability in nanodots. Néel skyrmions can be the ground state for dots of finite radius, whereas they can only be metastable in infinite films. The skyrmion stability area is extended by decreasing the out-of-plane anisotropy.