Lower Saxony's private train operating company Metronom already has a general alcohol ban running until November 15, the paper said.
Head of the national police union (GdP) Konrad Freiberg said he supported such a ban to prevent violence among football fans travelling to and from games.
“Where alcohol is in play, particularly among young people, it comes to property damage and assault more and more often,” he told the paper. “To some extent the costs are hardly bearable. A ban on buying alcohol in train stations – when for example football hoodlums are on their way – must be considered.”
Talks about such a ban are also reportedly on between Deutsche Bahn and the German Football Association, the paper said.