Schwarzer has been linked with a move to Premier League rivals Arsenal.
Hughes said: “From our point of view the situation has not changed. There was interest from Arsenal in May.
“Their bid was refused. We have not had any more bids and we wouldn’t encourage any.”
Hughes added: “Mark sees it as an opportunity with the current stage that he is at in his career.
“I can appreciate that but he has to understand that we have to protect Fulham too.
“At the moment it wouldn’t be right for Fulham football club.
“He is an outstanding goalkeeper. It’s only when you work with players that you realise how good they are.
“It would be difficult to replace him. It’s difficult to get the right quality into your football club. We have a top-class keeper in our squad and we would like to keep him.”
