Near-Earth Asteroids (NEAs) have attracted the attention of the scientific community in the last few years. Not only because of their importance to life on Earth but also their scientific potential and possible economic returns. This work explores the use of quasi-periodic orbits to bound the motion of NEAs close to the Earth’s vicinity for their exploitation. The invariant manifolds emanating from these quasi-periodic tori are used to design NEA high-thrust, low-energy retrieval trajectories. A thorough characterization of the two-dimensional space in which the invariant tori can exist is conducted. Three promising NEAs are selected, from which only two of them (2006 RH120 and 2020 CD3) permit transfers at extremely low ΔVs. For 2006 RH120, transfers that require between 20 and 2 times less ΔV than the existing results from literature were found. We prove that quasi-periodic orbits allow for better transfers than just considering manifolds from periodic families or not using manifolds at all. The use of quasi-periodic tori also permits extended transfer windows and more flexibility in the mission design.