Rail minister Paul Maynard said the proposal was one of a number of options being mooted to help improve passengers' access to compensation schemes.
The vast majority of compensation owed is not being claimed by passengers, he added.
Mr Maynard told the Daily Telegraph train companies could consider giving passengers delayed by 30 minutes or more details of how to claim in on-board announcements or in leaflets handed out by staff as they disembark.
He said: "I have been clear from day one that I want to make sure train operators put passenger interests first, and not just the convenience of the industry.
"There is no one recipe. I am keen to see a range of options to see which has most impact.
"In my meetings with the Rail Delivery Group I have been encouraging them all to think, 'How do I make the process of applying for compensation a simpler and easier process?'."
Earlier this month, Mr Maynard said passengers unhappy with their compensation - which currently varies between operators - would be able to pursue their claim through the courts if they failed to resolve the issue with the train company.
He said the Consumer Rights Act (CRA) introduced on October 1 last year should apply to all transport services, including mainline passenger rail services, from the beginning of next month.