Discs around young planets, so-called circumplanetary discs (CPDs), are essential for planet growth, satellite formation, and planet detection. We study the millimetre and centimetre emission from accreting CPDs by using the simple α disc model. We find that it is easier to detect CPDs at shorter radio wavelengths (e.g. λ ≲ 1 mm). For example, if the system is 140 pc away from us, deep observations (e.g. 5 h) at ALMA Band 7 (0.87 mm) are sensitive to as small as 0.03 lunar mass of dust in CPDs. If the CPD is around a Jupiter mass planet 20 au away from the host star and has a viscosity parameter α ≲ 0.001, ALMA can detect this disc when it accretes faster than 10−10M⊙yr−1⁠. ALMA can also detect the 'minimum mass sub-nebulae' disc if such a disc exists around a young planet in young stellar objects. However, to distinguish the embedded compact CPD from the circumstellar disc material, we should observe circumstellar discs with large gaps/cavities using the highest resolution possible. We also calculate the CPD fluxes at VLA bands, and discuss the possibility of detecting radio emission from jets/winds launched in CPDs. Finally we argue that, if the radial drift of dust particles is considered, the drifting time-scale for millimetre dust in CPDs can be extremely short. It only takes 102–103 yr for CPDs to lose millimetre dust. Thus, for CPDs to be detectable at radio wavelengths, mm-sized dust in CPDs needs to be replenished continuously, or the disc has a significant fraction of micron-sized dust or a high gas surface density so that the particle drifting time-scale is long, or the radial drift is prevented by other means (e.g. pressure traps).