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The understanding of organic content of protoplanetary discs is one of themain goals of the planet formation studies. As an attempt to guide theobservational searches for weak lines of complex species in discs, we modelledthe (sub-)millimetre spectrum of gaseous methanol (CH$_3$OH), one of thesimplest organic molecules, in the representative T Tauri system. We used 1+1Ddisc physical model coupled to the gas-grain ALCHEMIC chemical model with andwithout 2D-turbulent mixing. The computed CH$_3$OH abundances along with theCH$_3$OH scheme of energy levels of ground and excited torsional states wereused to produce model spectra obtained with the non-local thermodynamicequilibrium (non-LTE) 3D line radiative transfer code LIME. We found that themodelled 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 populationinversion occurs in the model calculations for many (sub-)millimetretransitions, it does not lead to the strong maser amplification and noticeablyhigh line intensities. We identify the strongest CH$_3$OH (sub-)millimetrelines 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 possiblybe detected with the $\sim5\sigma$ signal-to-noise ratio after $\sim3$ hours ofintegration with the full ALMA array.

Towards detecting methanol emission in low-mass protoplanetary discs with ALMA: The role of non-LTE excitation