A memorial service for the slain rapper was planned today at a Queens funeral home. The funeral will be Tuesday.
Senior police officials told The New York Times that the man had been feuding with Jay, whose real name was Jason Mizell, for as long as a decade.
Investigators said the man, whom they did not identify, had threatened one of Mizell's associates in a telephone call several weeks ago, the Times reported in Monday editions. They said the man announced that he was "coming up" from the South to resolve the conflict, but they did not know of any recent contact between the two men.
Mizell, 37, was shot by a masked gunman as he played video games Wednesday night in the lounge of his recording studio in Queens, New York.
A police spokeswoman, Detective Cheryl Cox, would not comment to The Associated Press about the report.
Meanwhile police continued to investigate the weekend slaying in the Bronx, New York of a man identified in media reports as a rap promoter. Kenneth Walker, 31, was shot several times in the back around 3 a.m. Saturday as he sat in his van.
Walker is said to have promoted Jay's protégé -- rapper 50 Cent. But detectives said they had no evidence to suggest Saturday's shooting was linked to Jay's murder.
The New York Post reports in its Saturday editions that the two slayings may be drawn into a larger probe by federal prosecutors of several players in the rap industry who they suspect of possible criminal conspiracy.
"They look at all rapper-related cases, which is why they're going to be looking at these two," a law-enforcement source told The Post.
The U.S. Attorney's Office in Manhattan has been weighing possible criminal-conspiracy charges against unnamed targets in the rap world for more than a year, the source told the newspaper.
The feds are probing links between rapper-related crimes - including two murders in The Bronx and New Jersey - and shootings, assaults and extortion in several boroughs, the Post said.
U.S. Bureau of Alcohol, Tobacco and Firearms agents are investigating how certain rappers and their associates acquired guns. And Internal Revenue Service agents are checking to see if rappers and their production companies are hiding assets and laundering money to avoid paying taxes, the Post reports.
The theory authorities are using, the source told the Post. is that some rappers and their hangers-on are acting as "an organized-crime group" whose nefarious and violent activities can be prosecuted under conspiracy statutes. "Like the Mafia," albeit "nowhere near as organized," the source said.