The cut-off rate analysis of hard-decision decoding and soft-decision decoding in additive white Gaussian noise (AWGN) channels reveals that 8-level signal quantization is adequate for most applications, and that there is little to be gained by increasing the precision any further towards pure soft-decision decoding with unquantized signals. In this paper, we seek to find if a similar conclusion can be drawn for the quantization of complex channel gain in time-variable flat fading environments, (channel quantization). In particular, we model the phase and/or amplitude of the flat fading channel as a finite state Markov (FSM) process, and propose the information capacity of FSM channel as a theoretical measure for choosing the number of channel quantization levels, as well as quantization thresholds. Recently proposed numerical methods enable us to efficiently compute the capacity of FSM channels for up to 16 states. Our results indicate that 8-level quantization is adequate in amplitude-only or phase-only quantization of the channel response, and that there is less than 0.3 dB to be gained by moving from 8 levels to 16 levels for a wide range of signal to noise ratios and channel fading rates. More emphasis is required for the quantization of phase in joint phase and amplitude quantization, and an 8-level phase and 2-level amplitude quantization is an optimum choice for a total of 16 channel quantization levels.