A number of League One and League Two clubs have registered an interest, but Bridges is set to seek a move further afield.
"We've agreed terms for Michael to go there until January and after that it's in his hands," City boss Phil Brown told the Hull Daily Mail.
"If he wants to stay he can, or he can come back here with the knowledge an Australian A-League side wants him and see what else is open to him.
"I'm just trying to shuffle my pack and allow the people I don't want in my squad to go and play football."