Permeability is generally measured at the core scale and only at a few sites. By using geostatistical techniques, one can generate alternative high-resolution images of the reservoir at the measurement scale. These images will honor both the data values at the data sites and some prior structural information as modeled, for example, by a covariance function. However, these images must be averaged to the scale of the flow-simulation gridblocks. Two questions arise: (1) how should averaging be carried out? and (2) could the gridblock values be generated directly from the core or log without the intermediary step of small-scale imaging? This paper proposes avenues to answer both questions. First, we propose an averaging technique from point to block permeabilities, accounting for the tensorial character of permeability. Second, we propose a method to infer the covariances and cross-covariances among the different components of the block permeability tensor, and the cross-covariances between these block values and the point measurements. This set of covariances and cross-covariances is then used to generate directly multiple, equally likely spatial realizations of gridblock permeability tensors conditioned to the point measurements. The method is not constrained by small variability of the underlying point permeability distribution, nor does it require a multi-Gaussian-related hypothesis.