  In this paper we study the entanglement properties of free {\em
non-relativistic} Bose gases. At zero temperature, we calculate the bipartite
block entanglement entropy of the system, and find it diverges logarithmically
with the particle number in the subsystem. For finite temperatures, we study
the mutual information between the two blocks. We first analytically study an
infinite-range hopping model, then numerically study a set of long-range
hopping models in one-deimension that exhibit Bose-Einstein condensation. In
both cases we find that a Bose-Einstein condensate, if present, makes a
divergent contribution to the mutual information which is proportional to the
logarithm of the number of particles in the condensate in the subsystem. The
prefactor of the logarithmic divergent term is model dependent.
