We observed the neutron star transient SAX J1810.8-2609 with Swift-XRT on November 3rd and 5th, in order to follow its way to quiescence. The source was not detected during the individual ~1.6 ksec and ~1.9 ksec observations. We place 95% upper limits on its 0.5-10 keV unabsorbed flux of [3.4-4.2]E-13 erg/cm2/s (November 3rd.) and [2.9-3.6]E-13 erg/cm2/s (November 5th.), where the range given corresponds to the uncertainty in the spectral model assumed (absorbing column density of 0.3E22 cm^-2 and a power law with index 2.5-1.5) and the prescription for low number statistics given by Gehrels (1986) has been applied.