The Naples natives reportedly went missing on January 31 after being detained by police at a gasoline station in Tecalitlan in southern Jalisco.
State authorities are “evaluating, using available information” whether police were involved in the disappearance, said Jalisco general secretary Roberto López.
He said state authorities will collaborate in the investigation with Mexico’s attorney general’s office and foreign ministry and the Italian Embassy in Mexico.
Lopez did not say if they were in direct contact with the relatives of the disappeared Italians.
Over the weekend family members and friends took to the streets of Naples to demand that Mexico’s government locate Raffaele Russo, Antonio Russo, and Vincenzo Cimmino.
Mexico is facing its worst-ever surge in violent crime, with more than 25,000 killings in 2017, as rival drug gangs splinter into smaller groups and dispute territory.
In Mexico’s most violent states, corrupt police officers often collude with criminal gangs.
The Jalisco New Generation Cartel, regarded by the United States as one of Mexico’s most powerful drug gangs, operates in Jalisco.