Eutectic gallium indium (EGaIn) is a liquid metal alloy at room temperature. EGaIn microdroplets can be incorporated into elastomers to fabricate highly stretchable, mechanically robust, soft multifunctional composites with high thermal stability(1) and electrical conductivity(2-4) that are suitable for applications in soft robotics and self-healing electronics(5-7). However, the current methods of preparation rely on mechanical mixing, which may lead to irregularly shaped micrometresized droplets and an anisotropic distribution of properties(8). Therefore, procedures for the stabilization of sub-micrometre-sized droplets of EGaIn and compatibilization in polymer matrices and solvents have attracted significant attention(9-12). Here we report the synthesis of EGaIn nanodroplets stabilized by polymeric ligand encapsulation. We use a surface-initiated atom transfer radical polymerization initiator to covalently functionalize the oxide layer on the surface of the EGaIn nanodroplets(13) with poly(methyl methacrylate) (PMMA), poly(n-butyl acrylate) (PBMA), poly(2-dimethylamino) ethyl methacrylate) (PDMAEMA) and poly(n-butyl acrylate-block-methyl methacrylate) (PBA-b-PMMA). These nanodroplets are stable in organic solvents, in water or in polymer matrices up to 50 wt% concentration, enabling direct solution-casting into flexible hybrid materials. The liquid metal can be recovered from dispersion by acid treatment. The nanodroplets show good mechanical, thermal and optical properties, with a remarkable suppression of crystallization and melting temperatures (down to -80 degrees C from 15 degrees C).