Police in the city — which is situated in the foothills of the Himalayas and next to the River Ganges — have said that they are treating the death as suspicious.
Local media have reported that the 52-year-old arrived in India on July 18th with his American girlfriend.
It said the couple had been travelled around the country and arrived in Varanasi on September 18.
Police chief Senior Superintendent Anand Kulkarni said that the man had been suffering from a severe bout of stomach pain on the night before he died.
He added that the death was being treated as suspicious and the matter had been referred to the British High Commission in New Dehli.
A spokesperson for Kashi Guest House said that staff informed police on Sunday night that the 52-year-old had fallen ill after complaining of of severe stomach pain.
He said that staff advised him to attend hospital but they claimed he wanted to stay in his room and by Monday morning he was found dead on the floor of the room with the door open.
A postmortem is expected to be complete in the coming days.