In this paper details of the experimental procedure and data analysis of the collision of 11 Be+ 64 Zn around the Coulomb barrier are described and discussed in the framework of different theoretical approaches. In a previous work [A. Di Pietro et al., Phys. Rev. Lett. 105, 022701 (2010).], the elastic scattering angular distribution of the collisions 9,10 Be+ 64 Zn as well as the angular distribution for the quasielastic scattering and transfer/breakup cross sections for the 11 Be+ 64 Zn reaction were briefly reported. The suppression of the quasielastic angular distribution in the Coulomb-nuclear interference angular region observed in the collision of the 11 Be halo nucleus with respect to the other two beryllium isotopes was interpreted as being caused by a long-range absorption owing to the long decay length of the 11 Be wave function. In this paper, new continuum-discretized coupledchannel calculations of the 11 Be+ 64 Zn reaction are reported in the attempt to interpret the effect of coupling with the breakup channels on the measured cross sections. The calculations show that the observed suppression of the Coulomb-nuclear interference peak is caused by a combined effect of Coulomb and nuclear couplings to the breakup channels.