If Verbeek has his way, Schwarzer and other England-based Socceroos will sit out the Premier League fixtures on the weekend of February 2/3 to enable them to link up with the Australia squad well ahead of an Asia Cup qualifier.
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.
"We know 100% that the European players can do that. If you play in the Italian Serie A, the English Premiership or the Bundesliga, we know they can handle that pressure.
"Whether it's realistic or not for Schwarzer to travel under those circumstances is another question," he added.