We study the feasibility of detecting preshower initiated by ultra-high energy photons using Monte-Carlo simulations of nearly horizontal air showers for the example of the La Palma site of the Cherenkov Telescope Array. We investigate the efficiency of multivariate analysis in correctly identifying preshower events initiated by 40 EeV photons and cosmic-ray dominated background simulated in the energy range 10 TeV -- 10 EeV. The effective areas for such kind of events are also investigated and event rate predictions related to different ultra-high energy photons production models are presented. While the expected number of preshowers from diffuse emission of UHE photon for 30 hours of observation is estimated around $3.3times10^{-5}$ based on the upper limits put by the Pierre Auger Observatory, this value is at the level of $2.7times10^{-4}$ ($5.7times 10^{-5}$) when considering the upper limits of the Pierre Auger Observatory (Telescope Array) on UHE photon point sources. However, UHE photon emission may undergo possible boosting due to gamma-ray burst, increasing the expected number of preshower events up to 0.17 and yielding a minimum required flux of $sim 0.2$ $mathrm{km^{-2}yr^{-1}}$ to obtain one preshower event, which is about a factor 10 higher than upper limits put by the Pierre Auger Observatory and Telescope Array (0.034 and 0.019 $mathrm{km^{-2}yr^{-1}}$, respectively).
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