So far, no real physical two dimensional (2D) monolayer materials with spin liquid (SL) state have been identified, although the SL state has been analytically predicted to be present in 2D triangular, honeycomb and kagome model lattices. Identifying a realistic monolayer, 2D SL material thus enables one to more clearly observe and understand the physics of the fractional quantum Hall effect, high-temperature superconductivity and magnetic monopole. In this work, we have performed first principles calculations within density functional theory to investigate the magnetic phase diagram in monolayer FeCl3, which reveals that the SL state may exist near the quantum phase transition between different antiferromagnetic (AFM) phases. Fundamentally, under a biaxial in-plane strain, the quantum phase transition appear and the ratio between the second neighboring exchange interaction (J 2) and the first neighboring interaction (J 1) falls into the SL range (0.21 ~ 0.28). Through comparison, the exchange energy ratio of monolayer FeBr3 (0.327 ~ 0.565) is beyond the SL range and thus FeBr3 could not exhibit SL characters. During the quantum phase transition induced by strain, the magnetic ground state transforms from AFM-Néel phase to AFM-stripy. Near the critical point, the semiconductor FeCl3 transforms from indirect to direct band gap. Our findings provide insights that the monolayer FeCl3 is a realistic 2D SL prototype material and the SL state could be observed by strain engineering.