After 28 years of service, Givney was dismissed last Friday along with football manager Darren Mooney, head trainer Mark Noakes and physiotherapist Konrad Schultz while coach Shane Flanagan was stood down.
The Sharks are under investigation by the Australian Sports Anti-Doping Authority (ASADA) over suspected doping practices at the club in 2011.
The Sharks board claimed their staff shake-up was not related to any use of banned substances, but rather "serious management failures" during a three-month period in 2011 when sports scientist Stephen Dank worked at the club.
Dank reportedly severed ties with the club after a clash with Givney.
The veteran doctor, who was also the Australian and NSW team medico during his career, said on Monday he has spoken to lawyers over his sacking.
"After meeting with my lawyer today I've decided to take legal action," Givney told The Australian.
"I have no desire to do anything to harm the club but I'm forced to leave matters in the hands of my lawyers at this time."
Noakes told ABC TV's 7.30 on Monday night that he hopes all the details regarding the club's recent management will soon come to light and he even holds out hope of being reinstated after the ASADA investigation is completed.
"To say I'm hurt would be an understatement. I'm just looking at reasons as to why they did it to all of us," he said.
"Whether it be them trying to save their skins - I'm not sure. That's just me. I'm just trying to come to terms with it.
"All these things that they said allegedly happened back in 2011 ... we didn't know anything was going wrong. So it's not like we were keeping them in the dark."