Arsene Wenger is keen to sign a new goalkeeper this summer to give Manuel Almunia and Lukasz Fabianski further competition, and they had a bid for 37-year-old Schwarzer - believed to be worth £2 million - rejected earlier this summer.
Fulham are said to have put a £4 million price tag on Schwarzer, but Hughes says Arsenal have yet to return with an improved offer and insists he has no interest in allowing him to leave Craven Cottage.
"From our point of view, the situation has not changed," he said. "There was interest from Arsenal in May. Their bid was refused. We have not had any more bids and we wouldn't encourage any.
"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."