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^{-10} M_{⊙} 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).
