Cross-correlation between the redshifted 21 cm signal and Lyman-{alpha} emitters (LAEs) is powerful tool to probe the Epoch of Reionization (EoR). Although the cross-power spectrum (PS) has an advantage of not correlating with foregrounds much brighter than the 21 cm signal, the galactic and extra-galactic foregrounds prevent detection since they contribute to the variance of the cross PS. Therefore, strategies for mitigating foregrounds are required. In this work, we study the impact of foreground avoidance on the measurement of the 21 cm-LAE cross-correlation. We then simulate the 21 cm observation as observed by the Murchison Widefield Array (MWA). The point source foreground is modelled from the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey catalogue, and the diffuse foreground is evaluated using a parametric model. For LAE observations, we assume a large survey of the Subaru Hyper Supreme-Cam (HSC), with spectroscopic observations of the Prime Focus Spectrograph (PFS). To predict the 21 cm signal, we employ a numerical simulation combining post processed radiative transfer and radiation hydrodynamics. Using these models, the signal-to-noise ratio of 2D PS shows the foreground contamination dominates the error of cross-PS even in the so-called `EoR window. We find that at least 99% of the point source foreground and 80% of the galactic diffuse foreground must be removed to measure the EoR signal at large scales $k<0.5 h rm Mpc^{-1}$. Additionally, a sensitivity 80 times larger than that of the MWA operating with 128 tiles and 99% of the point source foreground removal are required for a detection at small scales.
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