If no team claims the 27-year-old Bryzgalov, he'll be sent to Portland.
Bryzgalov, the backup to Jean-Sebastien Giguere, appeared in nine games this season. He was 2-3-1 with a 2.55 goals-against average and a .909 save percentage.
"He's been great. He has not asked for a trade," Ducks general manager Brian Burke said. "When we signed Hiller during the playoffs, you didn't hear a word out of Bryz. He's been terrific. He's a quality person who helped us win, then he deserves to go somewhere else and play."
The 25-year-old Hiller played in two games for the Ducks this season, going 1-1 with a 3.03 GAA and an .885 save percentage. He won his NHL debut, stopping 22-of-23 shots in Anaheim's 4-1 victory over the Los Angeles Kings on Sept. 30 in London.
Burke said he would be surprised if Bryzgalov isn't claimed during the 24-hour waiver period.
"I thought we had him traded at the draft," Burke said. "The other general manager left the room and went back and talked to his guys and backed off. I think it's commentary on lots of things -- the quality of goaltending in the league, the salary cap. Had we been able to retain some of his salary in a trade, we probably could have moved him. These are all factors."
The Ducks made Bryzgalov the 44th overall selection in the 2000 NHL draft. He appeared in 69 games with the Ducks, including a career-high 31 in the 2005-06 season, and has a 26-23-8 record with a 2.48 GAA.
Bryzgalov played in 11 games during the 2005-06 playoffs, going 6-4 with a 1.46 GAA.
Hiller, a native of Switzerland, has also played in six games for Portland this season, going 3-2-1 with a 2.11 GAA and a .929 save percentage. He was signed as a free agent last May after spending the 2006-07 season with Davos of the Swiss National League.