We consider a hybrid nanostructure composed of a semiconductor quantum dot placed near a spherical metallic nanoparticle, and study the effect of the nanoparticle on the population transfer from the ground state to the biexciton state of the quantum dot, when using linearly chirped Gaussian pulses. For various values of the system parameters (biexciton energy shift, pulse area and chirp, interparticle distance), we calculate the final population of the biexciton state by performing numerical simulations of the nonlinear density matrix equations describing the coupled system as well as its interaction with the applied electromagnetic field. We find that for relatively large values of the biexciton energy shift and not very small interparticle distances, the presence of the nanoparticle improves the biexciton state preparation, since it effectively increases the area of the applied pulse. For smaller biexciton energy shifts and smaller distances between the quantum dot and the nanoparticle, the exciton-plasmon interaction term gains importance leading in general to a degraded performance. But even in these cases we can still find ranges of parameter values where the population transfer to the biexciton state is accomplished with high fidelity, when using linearly chirped Gaussian pulses. We expect that these results may be exploited for the development of novel nanoscale photonic devices or future quantum technologies.