Gary Hutch, from Dublin, was chased and shot a number of times by a masked gunman at an apartment complex in Miraflores on Tuesday morning.
Irish police are working with Spanish authorities on the case and believe the murder is connected to a disagreement with a criminal gang.
Mr Hutch, who was 34, was a convicted armed robber had lived in Spain for the past eight years.
Irish state broadcaster RTÃ‰ has reported that he moved to the country after his release from prison and linked up with an organisation that Spanish police have said controls property and assets on four continents.
But he was believed to have fallen out with the group, RTÃ‰ has added.
Mr Hutch survived a number of previous attempts on his life.
A convicted Irish criminal has been shot dead in Spain's Costa del Sol.