Comets and asteroids offer insight into planetary formation, space resources exploitation, and collision mitigation techniques for planetary defence. On the other hand, the CubeSat paradigm, which led to a reduction in entry-level costs of more than an order of magnitude for low Earth orbit missions, is expected to be extended to interplanetary missions in the 2020s. The present work performs a preliminary trajectory analysis for a CubeSat mission departing from a geosynchronous transfer orbit to a near-Earth object, assuming a maximum mission duration of 3 years and an initial CubeSat mass of 16 kg. The goal is maximising the spacecraft final-to-initial-mass ratio for each of the trajectory concepts assessed. The Earth departure is modelled as multiple finite apogee raising manoeuvres, enabled by a high-thrust stage, leading to a parabolic escape. The interplanetary transfer is based on the patched conics method, and is modelled via: Lambert Problem impulsive manoeuvres at the Earth departure and target arrival, performed by the high-thrust stage, ending in a flyby or rendezvous; or a continuous low-thrust transfer, powered by the CubeSat, ending in a rendezvous. The low-thrust transfer concerns a smaller and less launch date dependent initial spacecraft mass, thus it tends to offer a lower launch cost, more piggyback flight opportunities, and greater launch date flexibility.