Magnetic skyrmions are widely attracting researchers due to fascinating physics and novel applications related to their non-trivial topology. Néel skyrmions have been extensively investigated in magnetic systems with Dzyaloshinskii–Moriya interaction (DMI) and/or perpendicular magnetic anisotropy. Here, by means of micromagnetic simulations and analytical calculations, we show that 3D quasi-skyrmions of Néel type, with topological charge close to 1, can exist as metastable states in soft magnetic nanostructures with no DMI, such as in Permalloy thick cylindrical and dome-shaped nanodots. The key factor responsible for the stabilization of DMI-free is the interplay of the exchange and magnetostatic energies in the nanodots. The range of geometrical parameters where the skyrmions are found is wider in magnetic dome-shape nanodots than in their cylindrical counterparts. Our results open the door for a new research line related to the nucleation and stabilization of magnetic skyrmions in a broad class of nanostructured soft magnetic materials.