The Australian international has revealed that there have been no new developments in his contract talks, meaning that a move could be on the cards.
The 40-year-old is looking to maintain first-team football as he looks towards next year's World Cup in Brazil.
"There's no new developments; there's no new discussions; there's no nothing," Schwarzer told reporters.
"I'm confident my club situation will resolve itself one way or another. Something will be sorted out - I've got no worries about that. I've got no idea at this stage where I'm going to be. I'm open to anything."
Schwarzer joined Fulham in 2008 after 11 years at Middlesbrough.