The 38-year-old wanted to leave Fulham to join Arsenal over the summer.
Schwarzer’s current contract with the Cottagers is set to expire at the end of the season.
“The saves he made – that’s the quality of the keeper we’ve got and that’s why we’re working so hard to keep him here,” Hughes said.
“If we’re going to be successful, we need a quality keeper and that’s certainly what Mark is.
“He knows what we provide and knows the environment very well. He’s not just got good players on the field of play, but a huge support staff behind him.
“He knows that the environment which has been created at Fulham is second to none.
“When you get to the latter stage of a career you have to be able to recover well and have all the up-to-date information in terms of recovery.
“What Mark has got is a real presence. With all the top keepers they have a presence and that permeates towards their team-mates.”
