The newspaper Welt am Sonntag quoted Udo Nagel, state interior minister of Hamburg, as saying the idea was among 22 recommendations on fighting juvenile delinquency prepared ahead of a meeting of state interior ministers this week.
"Truancy can be the beginning of a criminal career and that's why we have to intervene," said Nagel. "Not every truant becomes criminal, but criminals skipped school at one time or another."
Youths who cannot afford their own games play with consoles set up for demonstration purposes in city department stores and marts when they should be in school or at training courses.
Police suggested the consoles stay switched off every weekday until 3:00 pm, according to the report released Saturday.
The interior ministers of Germany's 16 states will discuss the proposal and other measures to fight youth crime at their spring conference in Brandenburg on April 16-18.