His partner Jennifer Platt is in in hospital in “serious but stable” condition after sustaining cuts and bruises in their hotel room.
The 40-year-old prop, who retired from the sport in 2012, collapsed early on Saturday morning while staying at the £350-a-night four-star Hotel Continentale in Florence.
Bibey, who worked as an estate agent, had only arrived with Ms Platt, 43, in the city of Manchester on Friday.
It was reported that the couple returned to their room “in good spirits” a few hours later around 2am.
It is not yet clear how Ms Platt, who also worked as an estate agent and has a child from a previous relationship, suffered her injuries and officers are waiting to question her.
A police source said: “We are working on two theories – an erotic game gone wrong or a domestic dispute. But the general meaning is that of an erotic game.”
“The man was found with a series of cuts, bruises and other injuries, as was the woman, although she was more seriously injured and the man appears to have had a seizure.”
“There is blood in the room and forensic teams are working on it.”
“The woman’s condition is serious but stable and her injuries are not life-threatening.”
Bibey has made 215 appearances for five rugby league clubs, including Wigan Warriors, Leigh Centurions and Wakefield Trinity – as well as three appearances for England A.
Wakefield Trinity said: ‘We are saddened to learn of Ricky’s passing. We extend our condolences to his family and friends. »
Leigh East, the amateur club where Bibey got his start as a junior, said: “All members of the club are saddened to hear of the passing.”
Leon Pryce, 40, a former St Helens, Bradford and Great Britain player, said: “Heartfelt condolences to Ricky’s family. We had been playing against each other since we were 14 years old. A great boy. Absolutely devastating news.
The Foreign, Commonwealth and Development Office said: ‘We are in contact with the Italian police.