If he goes unclaimed by noon ET on Thursday he'll be sent to San Antonio of the AHL.
"(Goalie coach) Grant Fuhr thinks that he needs to play some consecutive minutes, find his A game and get his confidence at a higher level," Coyotes GM Mike Barnett told The Canadian Press on Wednesday.
Barnett added that goalie David LeNeveu would be called up to replace Morrison as Curtis Joseph's backup.
Morrison went 0-3 in four starts this season with a 6.13 GAA and .790 save percentage. He was pulled during Tuesday night's 6-1 loss at Calgary.