The incident occurred on tracks near Loughborough Junction station, south London, which is an area popular with graffiti artists.
British Transport Police (BTP) were called to the scene at 7.30am on Monday but rail industry sources told the Press Association the paint was found nearby and the three people may have been killed overnight, when freight trains operate.
Officers were seen taking photographs of graffiti as part of their inquiries.
The bodies were found on an elevated section of track with an electric third rail between Brixton and Denmark Hill.
BTP stated that they were hit by a train but was unable to confirm whether it was a freight or passenger service. There were no reports of any passenger trains being involved.
Detective Superintendent Gary Richardson said: "My team are now working hard to understand what happened and how these three people came to lose their life on the railway.
"My thoughts are with the family and friends of these three people.
"At this time, we are treating their deaths as unexplained as we make a number of immediate inquiries.
"I would ask anyone who was near to Loughborough Junction this morning, and saw something which they think might be relevant, please contact us as soon as possible."
Rail regulator the Office of Rail and Road has opened a preliminary investigation.