gzip currently (version 1.9; released January 2018) does not support OpenCL.
Googling around (search string "gzip opencl"), I've found three OpenCL implementations of gzip: Altera and Xilinx both publish reference implementations for use with their FPGA, and WinZip also seems to support OpenCL.
Of the three, WinZip is closed source, and the Altera code is only licensed for use with Altera FPGAs, but the Xilinx code appears to be open source; they have a github repository at https://github.com/Xilinx/Applications. gzip however, is GPL code, so the Xilinx code is incompatible with its license agreement.
Probably the only way that gzip is going to get OpenCL support is for somebody to write a GPL OpenCL implementation of gzip.