  We investigate the deuteration of methanol towards the high-mass star forming
region NGC 7538-IRS1. We have carried out a multi-transition study of CH$_3$OH,
$^{13}$CH$_3$OH and of the deuterated fllavors, CH$_2$DOH and CH$_3$OD, between
1.0--1.4 mm with the IRAM-30~m antenna. In total, 34 $^{13}$CH$_3$OH, 13
CH$_2$DOH lines and 20 CH$_3$OD lines spanning a wide range of upper-state
energies (E$_{up}$) were detected. From the detected transitions, we estimate
that the measured D/H does not exceed 1$\%$, with a measured CH$_2$DOH/CH$_3$OH
and CH$_3$OD/CH$_3$OH of about (32$\pm$8)$\times$10$^{-4}$ and
(10$\pm$4)$\times$10$^{-4}$, respectively. This finding is consistent with the
hypothesis of a short-time scale formation during the pre-stellar phase. We
find a relative abundance ratio CH$_2$DOH/CH$_3$OD of 3.2 $\pm$ 1.5. This
result is consistent with a statistical deuteration. We cannot exclude H/D
exchanges between water and methanol if water deuteration is of the order
0.1$\%$, as suggested by recent Herschel observations.
