Reports have claimed Arsene Wenger could move for the 37-year-old after a string of high-profile errors from Manuel Almunia and Lukasz Fabianski last season.
But Schwarzer, currently in South Africa preparing to represent Australia at the World Cup, is unaware of any approach.
"I haven't heard anything other than what's been said or written in the papers, so it's purely speculative at the moment," he told ABC Sport.
"I've got another year left on my contract at Fulham and I've really enjoyed my time at Fulham and I'm enjoying it and I see my future at the moment with Fulham.
"I don't see anything changing unless someone tells me otherwise."