Arsenal tabled a £2m bid in May for the veteran Australian, who has handed in a transfer request, and they repeated the offer on Thursday. Hughes admits Schwarzer has been unsettled by the Gunners' interest but still hopes he will be a Fulham player at the end of the transfer window.
"There wasn't an improved offer from Arsenal - it was exactly the same one that was put forward in May," said the Welshman.
"The situation hasn't moved on. There's been contact but no improved offer.
"I don't know if Arsenal are trying to disrupt him. There are many things clubs, players and agents do to unsettle players.
"Mark is aware of the interest of Arsenal. That knowledge is distracting and disruptive.
"But the status quo is the same - we wouldn't encourage an improved bid. It's not at all inevitable he will leave."
Fulham are closing in on Benfica's Algeria defender Rafik Halliche in a deal reportedly worth £1.3m.
"There's still come paperwork to be concluded on the deal. We're hopeful it will go through quickly and we can finish it," said Hughes. "I saw him at the World Cup and I was aware of him even before that.
"It's always better to get a real opinion of a player when he comes through the door. Both he and Moussa Dembele, who we signed this week, are better than I initially thought which is a good sign."