Arsenal tabled a £2 million bid in May for the veteran Australian, who has handed in a transfer request, and on Thursday they repeated the offer. 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,'' Hughes said. "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 £1.3 million.
"There's still come paperwork to be concluded on the deal. We're hopeful it will go through quickly and we can finish it,'' Hughes said. "I saw him at the World Cup and I was aware of him even before that."
Almunia played in the opening game of the new Premier League season at Liverpool, where he made a crucial save from Steven Gerrard's free kick after a last-minute own goal by Reds goalkeeper Jose Reina hauled Arsenal level.
However, the Spaniard afterwards admitted the constant rumours surrounding his position were distracting, and hinted if an experienced stopper like Schwarzer came in then he would consider his own future at Emirates Stadium.
Wenger will keep faith with the 33-year-old for Saturday's visit of newly promoted Blackpool, but maintained no one player can be guaranteed a place in the starting XI.
"For us what is important at the moment in front of a big game is that we focus on the players we have,'' Wenger said. "Almunia is No. 1 - it is important that we give him the needed confidence, that we trust him, that we focus on tomorrow's game.
"It is a very sensitive subject which is difficult for me to talk about. You can understand that he is unsettled by that situation, but on the other hand, when you play at Arsenal, that is what you have to deal with.
"You have to be strong enough to deal with that and I believe he is. Jens Lehmann had to deal with that situation because at some stage I took him out of the team and played Almunia, so competition is part of our world. We have to accept that.''
Wenger, however, refused to be drawn on the Schwarzer situation.
"I never speak about the transfers, the offers, anything made about the players, because we have so many talks in football that are never concluded,'' he said. "It is always simple if you want to buy a player and the club doesn't agree: they say no, so there is not a lot to talk about.''