Givney, along with three other Sharks football staff member, were sacked by the club over their alleged cover-up of doping practices, while coach Shane Flanagan was stood down pending further investigation.
Elkin's legal team is exploring defamation litigation with regard to media reports over his involvement in the scandal.
"The last few weeks have been traumatic for my family and I and for many people at Cronulla," Elkin said.
"I am feeling very sad and distressed for the players and staff who are currently caught up in this.
"All I and they can hope for is a quick resolution to this matter for the sake of the individuals affected and the game as a whole.
"On the advice of my legal team, I have provided ASADA officials with a statement as part of their investigation and gave an honest account of the period in question.
"I have never condoned the use of performance enhancing drugs and I have not ever knowingly worked with anyone who did."
Among other denials from Elkin were that he concealed information on the Sharks' supplement program from Givney, and claims that he hid vials behind his back to avoid TV cameras in the Sharks dressing room.
Parramatta officials have continued to support Elkin, but denied playing any role in their trainer issuing Tuesday's statement.
The Cronulla players involved in the ASADA probe are set to be investigated next week, though the Nine Network reported on Tuesday night that Dank was refusing to meet with the players' lawyers.
Meanwhile there was no movement from the Sharks on Tuesday following reports the board - under new chairman Glenn Coleman - was set to make a final decision on the future of Flanagan.
It was claimed Flanagan may have been reinstated this week.
- AAP