Evan Nan Waring (56) was onboard the Delhi-Dibrugarh Rajdhani express with his friend Gerard Rafael when the incident happened on October 29.
Rafael told police that Evan was suffering from depression and was addicted to cigarettes.
GRP Inspector Tripurari Pandey said Rafael informed police that at around 4.15 am Evan went to smoke at the train's door from where he might have fallen while trying to open it.
Evan's son, who is in Japan, has sent a fax message to police saying the body should be handed over to Rafael as he can't come to India in such a short time to claim the body, he said.
GRP has asked Rafael to bring a no-objection certificate from the British embassy before handing over the body to him.
Evan's body was found on Howrah-Delhi railway track, around seven kilometres from central railway station here. The body had several deep wounds and a severed leg, police said, adding, a half-burnt cigarette was also found beside the body.