  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.
