Schwarzer was left out of the Fulham squad for their Premier League opener at the Reebok Stadium, just a day after it emerged that he had handed in a transfer request with a view to joining Arsenal.
That prompted speculation he may have been dropped, but Hughes said after the match that Schwarzer did not feature because he had failed a fitness test and confirmed he was still hoping to keep hold of the 37-year-old.
Asked if Schwarzer would be at Fulham much longer, Hughes said: "That is the intention, yes. Nothing has moved on.
"Myself and Mark have had conversations and I fully understand the reasoning behind the fact that he maybe wants to take up the opportunity (to join Arsenal).
"But I think he also understands that we have to protect our position as well, and that is what we are doing.
"We are not going to put Fulham's position or reputation at risk by making promises we can't fulfil, so at the moment it's very much the status quo and nothing has moved on."
Hughes is interested in signing Craig Bellamy - who played under him for Wales, Blackburn and the forward's current club Manchester City - but confirmed there had been no further developments on that front either.
"I said on Friday if there is an opportunity to bring him to the club, we will investigate that, but I'm aware that there are other clubs interested," Hughes said.
"Obviously we would like to do some things in terms of bringing him to the club, but there is a long way to go and the key to it is what Craig wants to do.
"I think it is really important that he takes the right step for him. I'm sure he will take his time and eventually come to the right decision."
Hughes' first competitive game in charge of Fulham was a low-key affair, his new side grinding out a point thanks in no small part to Schwarzer's replacement in goal, David Stockdale, who produced a string of fine saves on only his second Premier League appearance.
"I was pleased with what we produced today," Hughes said.
"You expect to have to deal with good quality here with the threat of Kevin Davies and I think we acquitted ourselves well, certainly the back five, and I include David Stockdale, who I thought played really, really well.
"The confidence that he showed helped the back four. They were very organised and understood what they needed to do to get a result today.
"David has been training well and I have been really impressed with him in the short time that I have been at the club.
"I had no qualms about throwing him in, I thought he'd do well and I'm glad that he has enjoyed the experience."
Bolton boss Owen Coyle, who saw midfielder Stuart Holden go closest to scoring with just over 10 minutes remaining by striking the post, was pleased with his side's performance but frustrated they could not make the most of their chances to secure victory.
"In terms of the opening day, there was an awful lot for me to be pleased about," Coyle said.
"We would have loved three points and I think at times we merited them.
"If we can continue to get clean sheets and have that cutting edge in the final third, that will result in points for us.
"Some of the play was great, the fans were fantastic, the atmosphere was great and just the disappointment is that we never got the win."