Guenther Platter is worried that Austria, who are members of the Schengen area where people travel without showing passports, may be targeted by those wanting to disrupt the finals.
Hooligans will be able to move about with relative ease and he wants organisers to impose a ban on known individuals to discourage them from travelling in the first place.
"We aim to survey the Schengen border temporarily at selected points but it makes no sense for us to survey the whole border or our other border crossings 24 hours a day," he said. "There is just not going to be complete control during the whole tournament."
Switzerland is not yet in the borderless Schengen area but is scheduled to join in October or November.
Some two million foreign fans are expected to descend on joint hosts Austria and Switzerland for Euro 2008, which will run from June 7 to 29.