Enhancement of sub-wavelength optical fields using sub-micron plasmonic probes has found many applications in chemical, material, biological and medical sciences. The enhancement is via localised surface-plasmon resonance (LSPR) which enables the highly sensitive vibrational-spectroscopy technique of surface-enhanced Raman scattering (SERS). Combining SERS with optical fibres can allow the monitoring of biochemical reactions in situ with high resolution. Here, we study the electromagnetic-field enhancement of a tapered optical fibre-tip coated with gold nanoparticles (AuNPs) using finite-element simulations. We investigate the electric-field enhancement associated with metallic NPs and study the effect of parameters such as tip-aperture radius, cone angle, nanoparticle size and gaps between them. Our study provides an understanding of the design and application of metal-nanoparticle-coated optical-fibre-tip probes for SERS. The approach of using fibre-coupled delivery adds flexibility and simplifies the system requirements in SERS, making it suitable for cellular imaging and mapping bio-interfaces.