The Australian has been pushed out of the first team picture since Brad Friedel moved to Ewood Park, and with Alan Kelly - also on the transfer list - he has been battling for the number two spot.
The 31-year-old met with manager Graeme Souness on Wednesday, and has now been placed on the transfer list in a bid to revive his career.
"I am disappointed," said Souness. "John is a good goalkeeper and currently in our squad, but I understand his frustration at not being in the team.
"I have told him we will not stand in his way but, with Alan Kelly in a similar situation, we can obviously only allow one of them to leave."
