The probe was first reported by TVA Sports in Montreal.
"The league did contact us [Monday] and we spoke to them," Murray said in a prepared statement. "Getzlaf did make ice available to teammates and paid a local coach, [who] ran it. There were no Ducks coaches present and hockey operations [staff] were all out of town."
The NHL's collective bargaining agreement with the players' union forbids teams to organize any workout or practice between Dec. 24-26.
If the league finds Murray's account is the case, it's believed the Ducks will avoid a violation of the collective bargaining agreement.
An NHL spokesman said the league wants to know whether Getzlaf was instructed to hold the practice.
It's unclear to Ducks officials how many players attended the workout at the team's practice facility.
After Monday's practice at Honda Center, Ducks defenseman Hampus Lindholm, center Rickard Rakell and forwards Rene Bourque, Devante Smith-Pelly and Emerson Etem each told The Times they knew nothing of an informal Dec. 26 practice and denied attending it.
The Ducks believe Getzlaf feared the four-day layoff could trigger rust, and took it upon himself to pay for the ice rental and the side coach.
"It's equal and all the same, I guess, we're all in the same boat," Getzlaf said after the Ducks' 2-1 shootout loss to the Arizona Coyotes on Saturday.
"You get out there, you're out of your rhythm a little bit. … You're still not as sharp as you'd like to be. The quality of the game showed that. I thought we played a pretty good game considering."