We report the results of simulations of magnetic skyrmion stability in ultrathin magnetic multilayer nanodots with interfacial Dzyaloshinskii–Moriya exchange interaction (DMI). We found that in presence of the lateral confinement the magnetostatic energy significantly influences the skyrmion stability and leads to stabilization of large-radius skyrmion even at low values of the DMI strength, in addition to small-radius skyrmion stabilized by DMI. In particular, stabilization of the skyrmion state with two different radii (bistability) is found in dipolarly-coupled (Pt/Co/Ir)n circular nanodots with the number of repeats of the unit cell n¼3 and 5. The bi-stability range is located at the DMI strength of 0.9–1.1 mJm2 or at the total Co-layer thickness of 2.2–2.6 nm.