GaN-based nanowires hold great promise for solid state lighting applications because of their waveguiding properties and the ability to grow nonpolar GaN nanowire-based heterostructures, which could lead to increased light extraction and improved internal quantum efficiency, respectively. In addition, GaN nanowires can be grown directly on Si substrates, providing an inexpensive and scalable platform for device fabrication. We use finite difference time domain photonic simulations to explore light extraction efficiency enhancement in GaN nanowire-based light-emitting diodes (LEDs) on Si. Emission polarization and the placement of the emission source along the length of the nanowire were taken into consideration. We find that the optimal placement of the emission source is determined by the light reflection at the nanowire-air and nanowire-substrate interfaces and the coupling of emitted radiation into the waveguided modes, resulting in extraction efficiencies of up to 50%. Our approach to optimizing light extraction via simulation techniques can be applied to more realistic large-scale devices to guide experimental work towards nanowire-based LEDs with potentially greater efficiencies than their thin-film counterparts.