Due to their orbits, near-Earth asteroids (NEAs) have been considered the most evident parent bodies of meteorites. Dynamical models show that NEAs come primarily from the inner and central parts of the Main Belt (MB), and they reach their orbits by means of gravitational resonances (mainly ?6 and 3:1). This part of the MB is dominated by spectral types S and Q, also the most common spectral types among the NEA population (~60%), and correspond to objects composed of silicates. Their reflectance spectra show very characteristic absorption bands that can be used to infer their mineralogical composition applying different methods of analysis. Those absorption bands are also present in the spectra of the most abundant class of meteorites (~80%), the ordinary chondrites (OC). In order to better understand the connection between MB asteroids, NEAs and OCs, we undertook a spectroscopic survey of asteroids between 2002 and 2007, using the telescopes and instrument facilities of "El Roque de los Muchachos" Observatory, in the Canary Islands. The survey contains visible and near-infrared spectra (0.5 - 2.5 µm) of a total of 105 asteroids. We have applied a method of mineralogical analysis based on spectral parameters to our sample of NEAs, and also to a sample of 91 MBs and 103 OCs obtained from different databases. We have found some significant compositional differences between NEAs, MBs and OCs. The most remarkable one is that NEAs compositionally differ from the whole set of OCs, and show a more olivine-rich composition, similar to what it is found for LL chondrites (only 8% of the falls). This result suggests that S type NEAs are not the immediate precursors of ordinary chondrites, as it was believed. We consider the size of the objects as the key factor to explain this difference. NEAs are km-sized objects, while meteorites are meter tocm sized objects. Combining the information obtained from the dynamical models and the drift in semimajor axis of the smaller objects due to their thermal intertia (Yarkovsky effect), we set out a possible scenario for the formation and the transport routes of NEAs and meteorites that could explain this compositional difference in a plausible way.