  The existence of intermediate-mass ($\sim 10^3 M_\odot$) black holes in the
center of globular clusters has been suggested by different observations. The
X-ray sources observed in NGC 6388 and in G1 in M31 could be interpreted as
being powered by the accretion of matter onto such objects. In this work we
explore a scenario in which the black hole accretes from the cluster
interstellar medium, which is generated by the mass loss of the red giants in
the cluster. We estimate the accretion rate onto the black hole and compare it
to the values obtained via the traditional Bondi-Hoyle model. Our results show
that the accretion rate is no longer solely defined by the black hole mass and
the ambient parameters but also by the host cluster itself. Furthermore, we
find that the more massive globular clusters with large stellar velocity
dispersion are the best candidates in which accretion onto IMBHs could be
detected.
