Magnetoelectric (ME) composite materials, in which the coupling between magnetostricitve and piezoelectric effects is achieved, are potential candidates for multifunctional devices where the interplay between electrical, magnetic and mechanical properties of these structures can be fully exploited. Nanostructured composites are particularly interesting due to the enhancement of ME coupling expected at the nanoscale. However, direct studies of ME coupling in nanocomposites by scanning probe techniques are rare due to the complex interplay of forces at play, including those arising from electrostatic, magnetic and electromechanical interactions. In this work, the ME coupling of coaxial nickel - polyvinylidene fluoride trifluoroethylene [Ni-P(VDF-TrFE)] composite nanowires, fabricated by a scalable template-wetting based technique, is studied using a systematic sequence of scanning probe techniques. Individual ME nanowires were subjected to an electric field sufficient for ferroelectric poling in piezo-response force microscopy (PFM) mode, while magnetic force microscopy (MFM) was used to measure localised changes in magnetization as a result of electrical poling. Kelvin probe force microscopy (KPFM) measurements of surface potential were conducted to eliminate for the effect of contact potential differences during these measurements. An inverse, static, magnetoelectric coupling coefficient of ~1 x 10-11 s m-1 was found in our coaxial nanocomposite nanowires, comparable to other types of planar composites studied in this work, despite having an inferior piezoelectric-to-magnetostrictive volume ratio. The efficient ME coupling in our coaxial nanowires is attributed to the larger surface-to-volume interfacial contact between Ni and P(VDF-TrFE), and is promising for future integration into ME composite devices such as magnetic field sensors or energy harvesters.