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.
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