[Update: A man is being questioned in the killing of the Gambino boss.]

While Gene Gotti was in prison in the 1990s, he hatched a plan with a Gambino family associate: They would keep up a strict workout routine at the prison gym, federal agents learned. They had to stay in shape, Mr. Gotti reportedly said, because once they got out, he was going to retake control of the Gambino enterprise.

This week, that exchange took on new significance. Late Wednesday, the acting boss of the Gambino crime family, Francesco Cali, was shot dead outside his Staten Island home, just six months after Mr. Gotti had been released from federal custody.

Police commanders said on Thursday that it was too early in the investigation to determine if Mr. Cali’s killing was related to Mr. Gotti’s release, or was mob-related at all. But one avenue of investigation remains the possibility of an internal war among family associates, former law enforcement officials said.

Mr. Cali represented a new chapter in the Gambino family’s history. He was part of a Sicilian faction that took over the family in 2011, when Domenico Cefalù rose to be the acting boss. Both Mr. Cefalù and Mr. Cali had tapped networks in Palermo, Sicily, for foot soldiers, and they adopted a quieter approach to their business dealings.