In this paper, we use radiative transfer+N-body simulations to explore the feasibility of measurements of cross-correlations between the 21-cm field observed by the Square Kilometre Array (SKA) and high-z Lyman α emitters (LAEs) detected in galaxy surveys with the Subaru Hyper Suprime-Cam (HSC), Subaru Prime Focus Spectrograph (PFS), and Wide Field Infrared Survey Telescope (WFIRST). 21cm–LAE cross-correlations are in fact a powerful probe of the epoch of reionization as they are expected to provide precious information on the progress of reionization and the typical scale of ionized regions at different redshifts. The next generation observations with SKA will have a noise level much lower than those with its precursor radio facilities, introducing a significant improvement in the measurement of the cross-correlations. We find that an SKA-HSC/PFS observation will allow to investigate scales below ∼10 and ∼60 h −1 Mpc at z = 7.3 and 6.6, respectively. WFIRST will allow to access also higher redshifts, as it is expected to observe spectroscopically ∼900 LAEs per deg 2 and unit redshift in the range 7.5 ≤ z ≤ 8.5. Because of the reduction of the shot noise compared to HSC and PFS, observations with WFIRST will result in more precise cross-correlations and increased observable scales.