Law enforcement sources told the newspaper detectives believed the actor acted in self-defense.
The suspect -- identified as Jonathan Kirby, 56, a transient with a lengthy arrest record for thefts, fights and drugs -- was hospitalized after what police sources told the Times was a "knock-down, drag-out" fight.
Kirby was arrested on suspicion of burglary and may face a battery charge, the Times said Thursday.
Gossip Web site TMZ said Kirby was charged with first-degree burglary with a person present, and could face 38 years to life in prison.
The site said the Los Angeles County District Attorney's Office charged Kirby as a third-strike offender under California's 1994 "three strikes" law, which mandates that state courts impose sentences as much as to life in prison on people convicted of three or more serious criminal offenses.
Serious offenses include burglary of a residence and assault with intent to commit a robbery.
"LL Cool J, and his family, are safe and thank everyone for their thoughts and concern," a spokesman said in a statement Wednesday after the incident. "As a father, husband and citizen, he is committed to keeping his family safe and is cooperating with authorities on this private matter."
LL Cool J -- who was born James Todd Smith -- said he had gone downstairs when he heard noise in the kitchen area at his home and the suspect came at him. When police arrived around 1 a.m. PDT Wednesday, the rapper-actor had detained the battered and bruised Kirby, police said.
LL Cool J plays former U.S. Navy SEAL Senior Field Agent Sam Hanna on the CBS drama series "NCIS: Los Angeles." Among his hip-hop hits is "Mama Said Knock You Out," from his album of the same name, released in 1991.