  The understanding of organic content of protoplanetary discs is one of the
main goals of the planet formation studies. As an attempt to guide the
observational searches for weak lines of complex species in discs, we modelled
the (sub-)millimetre spectrum of gaseous methanol (CH$_3$OH), one of the
simplest organic molecules, in the representative T Tauri system. We used 1+1D
disc physical model coupled to the gas-grain ALCHEMIC chemical model with and
without 2D-turbulent mixing. The computed CH$_3$OH abundances along with the
CH$_3$OH scheme of energy levels of ground and excited torsional states were
used to produce model spectra obtained with the non-local thermodynamic
equilibrium (non-LTE) 3D line radiative transfer code LIME. We found that the
modelled non-LTE intensities of the CH$_3$OH lines can be lower by factor of
$>10$--$100$ than those calculated under assumption of LTE. Though population
inversion occurs in the model calculations for many (sub-)millimetre
transitions, it does not lead to the strong maser amplification and noticeably
high line intensities. We identify the strongest CH$_3$OH (sub-)millimetre
lines that could be searched for with the Atacama Large Millimeter Array (ALMA)
in nearby discs. The two best candidates are the CH$_{3}$OH $5_0-4_0~A^+$
(241.791 GHz) and $5_{-1}-4_{-1}~E$ (241.767 GHz) lines, which could possibly
be detected with the $\sim5\sigma$ signal-to-noise ratio after $\sim3$ hours of
integration with the full ALMA array.
