  Context. The high intensities and narrow bandwidths exhibited by some
astronomical masers make them ideal tools for studying star-forming giant
molecular clouds. The water maser transition $J_{K_{-1}K_{1}}=5_{32}-4_{41}$ at
620.701 GHz can only be observed from above Earth's strongly absorbing
atmosphere; its emission has recently been detected from space. Aims. We sought
to further characterize the star-forming environment of Orion KL by
investigating the linear polarisation of a source emitting a narrow 620.701 GHz
maser feature with the heterodyne spectrometer HIFI on board the Herschel Space
Observatory. Methods. High-resolution spectral datasets were collected over a
thirteen month period beginning in 2011 March, to establish not only the linear
polarisation but also the temporal variability of the source. Results. Within a
$3\sigma$ uncertainty, no polarisation was detected to an upper limit of
approximately 2%. These results are compared with coeval linear polarisation
measurements of the 22.235 GHz $J_{K_{-1}K_{1}}=6_{16}-5_{23}$ maser line from
the Effelsberg 100-m radio telescope, typically a much stronger maser
transition. Although strongly polarised emission is observed for one component
of the 22.235 GHz maser at 7.2 km s$^{-1}$, a weaker component at the same
velocity as the 620.701 GHz maser at 11.7 km s$^{-1}$ is much less polarised.
