The current paradigm in General Relativity (GR), Quantum Mechanics (QM), and Quantum Field Theory (QFT) is that the physical laws must be invariant under Lorentz transformations. However, some theories aiming at unifying GR and QM (such as Quantum Gravity (QG) and string theory) allow Lorentz Invariance Violation (LIV) at the Planck scale ($\sim 10^{-35}$ m, $\sim 10^{19}$ GeV), potentially leading to several observable consequences. Due to a modified energy-momentum dispersion relation for photons, LIV effects might be identified by searching for time delays in the TeV gamma-ray photons coming from distant and highly variable astrophysical sources, such as relativistic outflows from pulsars, Gamma-ray Bursts (GRBs), and Active Galactic Nuclei (AGN). In particular, blazar jets possess the desired characteristics to search for LIV effects. Using the AGN Evolution Simulator (AGNES) code, the broadband spectra of a blazar can be modeled by using a time-dependent one-zone Synchrotron-Self-Compton (SSC) scenario during a flaring state, and the presupposed LIV delays can be introduced alongside the intrinsic time-lags from the source. In this work, we aim to analyze the capacity of the Cherenkov Telescope Array (CTA) to detect global time delays and to discriminate between the contribution of intrinsic phenomena in the jet and possible LIV effects. The methodology and preliminary results from the simulations performed for the feasibility studies with CTA are presented.