According to the Mirror, the briefing note was found on the floor of a first-class carriage on a train heading from Manchester to Edinburgh in January.
The document identified details such as a private address where Theresa May was attending a dinner that evening.
A Cabinet Office spokeswoman said they had been made aware of the claims.
The two-page briefing note was found by a member of the public at around midday on the day of the trip, the Mirror said.
‘Serious security breach’
A government spokesman said: “We have been made aware of claims around a government document and will investigate accordingly.”
A former royal bodyguard, Inspector Ken Wharfe, told the Mirror it was a serious security breach.
He said: “In today’s environment, it becomes a serious security matter when documents like this detailing the hourly movements of a protected person are misplaced. That’s just not acceptable.”