Didn't Lucky Luciano offer FDR a deal on the invasion of Sicily (and then Italy)?
stay safe.
No. The Defense Department actually approached Luciano with a deal. Luciano had been convicted on a number of (some say bogus) charges of "compulsory prostitution", and was doing 30 years at Dannemora prison in New York. Luciano also controlled the dock workers unions in New York City. The government wanted information on possible German spies trying to sabotage ships in the harbor, and the only way to get it was through Luciano.
So they made him a deal, and offered him deportation back to Sicily in exchange for his help. He also provided assistance to the Defense Department during the invasion of Sicily, by getting locals to cooperate with Allied powers.
He continued to control business in the US even while in Sicily, including running casinos in Las Vegas. In the movie "Godfather II", there's a meeting in Havana to discuss the casinos. This meeting actually happened. It was heads of various families, Myer Lansky, and Charles "Lucky" Luciano, who got that nickname after being beaten, stabbed and shot by rival gang members and he still lived.
The front for the Havana meeting was that it was a birthday party for Frank Sinatra, who also was in attendance.
Interestingly, Time magazine included Luciano in its list of the "100 Most Influential Business Geniuses of the Century".