A system of permanent magnet quadrupoles (PMQs) is going to be realized by INFN-LNS to be used as a collection system for the injection of laser driven ion beams up to 60 MeV/u in an energy selector based on four resistive dipoles. This system is the first element of the ELIMED (ELI-Beamlines MEDical and Multidisciplinary applications) beam transport, dosimetry and irradiation line that will be developed by INFN-LNS (It) and installed at the ELI-Beamlines facility in Prague (Cz). ELIMED will be the first user's open transport beam-line where a controlled laser-driven ion beam will be used for multidisciplinary researches. The definition of well specified characteristics, both in terms of performances and field quality, of the magnetic lenses is crucial for the system realization, for the accurate study of the beam dynamics and for the proper matching with the magnetic selection system which will be designed in the next months. Here, we report the design of the collection system and the adopted solutions in order to realize a robust system form the magnetic point of view. Moreover, the first preliminary transport simulations are also described.