Australian is keen to play in the Champions League with the Gunners
Gunners boss Arsene Wenger has already had a £2 million offer for the Australia international goalkeeper rejected by the Cottagers this summer.
Wenger is looking to replace Manuel Almunia with a steady, veteran keeper like Schwarzer, who at 37-year-old is hoping to experience Champions League football for the first time.
However, Hughes insists that he has no interest in top players like Schwarzer and Paul Konchesky, who Liverpool are interested in signing, before the new Premier League season begins.
“There is always interest in quality players and it is not my intention to allow the betters players leave the football club," Hughes told The Mirror.
“We are in a position where we don't have to sell our better players.
“We want to progress and you want to have the better players, so I suggest the two players you mention will still be Fulham players by the end of the window.
"There was a conversation [with Schwarzer] some time ago but I have only just come through the door and will have to refresh myself about the conversations that happened.
"But we want to resolve the situation as soon as possible but we are not in the position of letting our best players leave and Mark falls into that category.”