  Galaxy clusters are expected to gravitationally lens background radio
sources. However, due to the smaller surface density of radio sources, when
compared to optical galaxies, such lensed events are rare. For an example, it
is expected that there is no lensed radio source due to foreground galaxy
clusters in the 1.4 GHz VLA FIRST survey. However, at the $\mu$Jy level, the
surface density of radio sources increases. Using the radio properties of the
Hubble Deep Field (HDF) galaxies, we calculate the expected number of
gravitationally lensed $\mu$Jy rad io sources on the sky due to foreground
galaxy clusters for different cosmological models. For a flat cosmology with
$\Omega_m=0.3$ and $\Omega_\Lambda =0.7$, we predict $\sim$ 1500 lensed radio
sources with flux densities $\sim$ 10 to 1000 muJy at 1.4 GHz. We discuss the
possibility of detecting lensed muJy radio sources towards clusters with deep
radio surveys. Given the recent detection of a sub-mm selected lensed muJy
radio source towards A370, it is suggested that deep radio observations of
clusters should already contain such lensed sources. Aided by amplification due
to gravitational lensing, the search for lensed \muJy radio sources towards
clusters are likely to recover star-forming galaxies at redshifts of 1 to 3.
