According to Catalan newspaper, La Vanguardia, the former rugby player had built up a vast debt due to his “frenzied lifestyle”.
Such was his debt that Mr Davis feared he would be poisoned by the mafia, the paper claimed.
A member of the team of private detectives hired to find Mr Davis was quoted as saying: “Davis came to Barcelona fleeing from these criminals. He had adopted a frenzied lifestyle and was in a very delicate situation.
“The truth is he was sure they were chasing him. In fact he was convinced they had tried to poison him on one occasion.”
The report comes as the Spanish police have been asked to look into a possible drowning in Barcelona’s port hours after Mr Davis was last seen.
Local authorities later confirmed that his passport was found in the same area after a man was seen in distress in the water.
Good Morning Britain reporter, Nick Dixon said: “A man was in the water in distress in the port area close to a nearby cruise ship.
“A search was carried out but no body was found and everyone was accounted for, at least on the cruise ship.
“But it was some time later that the police realised Levi's passport was found in that same area.”
Mr Davis had been staying with friends in Ibiza before he travelled to Barcelona.
After being seen on CCTV, he is believed to have walked northwards on La Rambla to the Hard Rock Café where the trail has gone cold.
Mr Davis had played Premiership rugby for Bath between 2017 and 2020 and starred on Celebrity X Factor in 2019 alongside Ben Foden and Thom Evans. He was also on E4's Celebs Go Dating in 2020.