Chromatic dispersion is one of the error sources limiting the transmission capacity in coherent optical communication that can be mitigated with digital signal processing. In this paper, the current status and plans of implementation of chromatic dispersion compensation (CDC) filters on FPGAs are discussed. As these high-speed filters are most efficiently implemented in the frequency-domain, different approaches for high-speed FFT-based architectures are considered and preliminary results of fully parallel FFT implementation by utilizing FPGA hardware features are presented.