Room-temperature stabilization of skyrmions in magnetic multilayered systems results from a fine balance between several magnetic interactions, namely, symmetric and antisymmetric exchange, dipolar interaction and perpendicular magnetic anisotropy as well as, in most cases, Zeeman through an applied external field. Such field-driven stabilization approach is, however, not compatible with most of the anticipated skyrmion based applications, e.g., skyrmion memories and logic or neuromorphic computing, which motivates a reduction or a cancellation of field requirements. Here, we present a method to stabilize at room-temperature and zero-field, a densely packed skyrmion phase in ferromagnetic multilayers with moderate number of repetitions. To this aim, we finely tune the multilayer parameters to stabilize a dense skyrmion phase. Then, relying on the interlayer electronic coupling to an adjacent bias magnetic layer with strong perpendicular magnetic anisotropy and uniform magnetization, we demonstrate the stabilization of sub-60 nm diameter skyrmions at zero-field with adjustable skyrmion density.