His deal ends in June and he is ready to tough it out at Craven Cottage before signing a pre-contract in January with a top European club and walking away for free.
He will also head for the Asia Cup with Australia in January, meaning he will miss a month of Premier League action despite previously indicating that he would give the tournament a miss.
Schwarzer, 37, claims a transfer request was sent to Fulham on email but the club deny any record of the demand.
Hughes has told close aides he will only sell if Manchester City let him have Shay Given on loan.