We investigate the deuteration of methanol towards the high-mass star-forming region NGC 7538-IRS1. We carried out a multi-transition study of CH₃OH, ¹³CH₃OH, and the deuterated flavors, CH₂DOH and CH₃OD, between 1.0 and 1.4 mm with the IRAM-30 m antenna. In total, 34 ¹³CH₃OH, 13 CH₂DOH lines and 20 CH₃OD 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 CH₂DOH/CH₃OH and CH₃OD/CH₃OH of about (32 ± 8) × 10⁻⁴ and (10 ± 4) × 10⁻⁴, respectively. This finding is consistent with the hypothesis of a short-timescale formation during the pre-stellar phase. We find a relative abundance CH₂DOH/CH₃OD ratio of 3.2 ± 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.