A 1958 "secret" FBI document which recently has been "declassified" discloses that the G-men were considering planting bugs in the apartments maintained by Meyer Lansky and Santo Trafficante at the Hotel Nacional de Cuba.
Lansky and Trafficante were high-value targets for the FBI for their gambling operations in Cuba where they maintained a corrupt relationship with dictator Batista, and the now-declassified May 20, 1958 memo from Frank Price, the chief of the criminal section, to Alex Rosen, the assistant director of the investigative division, characterizes the two mobsters as follows:
Both Lansky and Trafficante are extremely important top hoodlums. Trafficante was at the Apalachin meeting on 11/14/57, and was the only person there known to have attempted to conceal his true identity from the police when questioned. He is also the person who was dealing with the late Albert Anastasia in connection with the gambling casino in the Havana-Hilton Hotel and was with Anastasia the evening before Anastasia was murdered.
Because of the foregoing and the reputation of Lansky as being the top American figure in Cuban gambling activities, there has been considerable public speculation that Anastasia was murdered and the meeting at Apalachin was held because of circumstances surrounding the gambling activities in Cuba. There has been speculation that Trafficante was representing Lansky, both in his meeting with Anastasia and in his attendance at Apalachin.
The potential value of a microphone surveillance, particularly in Lansky's apartment, is tremendous. From past information from the Legal Attache, it appears that Lansky visits gambling establishments in which he is interested with infrequency and apparently other important hoodlums in Cuba call on him at his residence apartment on business matters.
That the subject hoodlums (Lansky and Trafficante) enjoy the protection and wield influence in the Batista Government is not doubted as all American gambling elements in Cuba must pay off the Batista Government.
The proposal to bug Lansky and Trafficante at their Cuban apartments apparently would be coordinated by the FBI's Miami Field Office with the Legal Attache and may include a CIA role. Of course, the involvement of the embassy and the CIA was problematic as the 1958 memo aptly notes:
In passing upon the recommendations in this memorandum, it should be noted that the Legal Attache's office in Cuba is, by agreement with the Department of State, a liaison post and is not operational in scope. It is held out to be and is an integral part of the American Embassy. Any embarrassment to the Legal Attache's office not only places the Bureau in a bad light but could automatically become an international incident.
From referenced letter, it appears that the Legal Attache may be considering use of a CIA employee's apartment in the same building for obtaining coverage. This is undesirable at best as we should not, unless absolutely essential, run joint operations with the CIA. If we were to do so, CIA headquarters would have to be consulted and clearance obtained prior to approaching any CIA employee. By its charter, CIA could and probably would consider such a foreign information collection within its jurisdiction.
Discovery of this installation could result in grievous consequences and a possibility that the Legal Attache and his staff would be considered non grata by the Cuban Government, which would be most embarrassing to the Bureau and to the United States Government. *** Further, under no circumstances and at no time would the information obtained by such coverage be utilized as evidence as to do so would compromise the liaison status of the Legal Attache;s office and conclusively show the Bureau’s violation of Cuban sovereignty.
It's unclear whether the G-men ever followed through in actually bugging the Cuban apartments of Lansky and Trafficante.