If anyone denies that the FBI hierarchy didn't voice their opinions about killing the gangsters, this memo about "knocking off" "Pretty Boy" Floyd  may remove all doubt.  And it looks like Assistant Director to Hoover, E. A. Tamm, made it very clear.  Unusual?  Probably not.

After all, Floyd was allegedly involved in multiple violent crimes including the killing of law enforcement officers.

What is interesting is perhaps SAC Fay's recommended use of SA Jack Keating who obviously had serious eye problems and surely wasn't fit for any confrontation with Floyd or anyone else for that matter.  You can see Hoover's penned comment that he wasn't too happy with this decision. 

While this particular sighting or lead on Floyd didn't materialize, Floyd was later killed in October, 1934.

See the memo here