The person spoke Sunday on the condition of anonymity because the team has not announced the decision.
Bryzgalov hasn't played since allowing three goals on eight shots in a 6-2 loss at Florida on Feb. 10. The 34-year-old went 1-4-1 in eight appearances since signing a one-year, $2.88 million contract with Anaheim in December.
Gibson has played six games since being recalled Feb. 10 following a two-month stint in the minors. Andersen is day to day after missing six games with an upper-body injury.