FPGA based theremin , is possible?
The short answer is yes, although it's really not a good fit for an FPGA project and the FPGA is mostly useless.

Fundamentally a Theremin is a capacitative sensor device like a smartphone's touchscreen or proximity sensor, but tuned to very high sensitivity. See this Arduino theremin, which would be a good basis to adapt from. There may be capsense libraries or IP cores for your FPGA which would make is easier.