  Short-period planets suffer from extreme tidal forces from their parent stars
causing them to deform and attain non-spherical shapes. The planet shapes,
modeled here as triaxial ellipsoids, can have an impact on the observed transit
light curves and the planetary parameters derived. We investigate the
detectability of tidal deformation in short-period planets from their transit
light curves and the instrumental precision needed. We show how the detection
of deformation from the light curve allows us to obtain an observational
estimate of the second fluid Love number which gives valuable insight about the
planet's internal structure. We adopted a model to calculate the shape of a
planet due to the external potentials acting on it and used this model to
modify the ellc transit tool. Our model is parameterized by the Love number,
hence for a given light curve we can derive the value of the Love number that
best matches the observations. We simulated the known cases of WASP-103b and
WASP-121b expected to be highly deformed. Our analyses showed that instrumental
precision $\leq$50ppm/min is needed to reliably estimate the Love number and
detect tidal deformation. This precision can be achieved for WASP-103b in ~40
transits using HST and in ~300 transits using the forthcoming CHEOPS. However,
fewer transits will be required for short-period planets that may be found
around bright stars in the TESS and PLATO survey missions. The unprecedented
precisions expected from PLATO and JWST can permit the detection of deformation
with a single transit. However, the effects of instrumental and astrophysical
noise must be well-considered as they can increase the number of transits
required to reach the 50 ppm/min detection limit. We also show that improper
modeling of limb darkening can act to bury signals related to the planet's
shape thereby leading us to infer sphericity for a deformed planet.
