Neither police or the newspaper confirmed whether Vargas, 60, had been under police guard at the 12 October hospital in the Spanish capital.
In the 1980s Vargas, allegedly a former partner of Pablo Escobar, the late Medellin cartel drug chief, ran his own cocaine manufacturing and smuggling operation out of a remote, jungle-covered area of Colombia's southwestern Caqueta province.
A Colombian court sentenced him in 1995 to 26 years in prison for illicit enrichment related to drugs, but he was freed in 2002.
Spanish authorities arrested him for carrying a fake Venezuelan passport in 2006 and he was awaiting trial in connection with a 500kg cocaine haul.
His trial had been delayed and prison authorities freed him after he came down with what Spanish media said was a lung-related illness.
Police believe his killing was a settling of scores by drug rivals.