The Dutchman wants all of his key players, including the Boro shot-stopper, in his squad for the match against Qatar in Melbourne on February 6.
However Gareth Southgate is only obliged to release his keeper 48 hours before the Asia Cup tie and is sure to want Schwarzer in his line-up to face Newcastle at St James' Park.
Verbeek told the Evening Gazette: "All the European-based players have told me they are desperate to come.
"I don't know yet whether we have enough A-League players who can play to their top form in that sort of pressure situation.
"Whether it's realistic or not for Schwarzer to travel under those circumstances is another question," he added.