The firefighter was hurt, but not critically, when he fell through the third floor landing down to the first floor while battling the blaze at 1793 Sedgewick Avenue.
An investigator, speaking on the condition of anonymity, said a homeless man might have been sleeping on a couch in the hallway and was possibly torched -- sparking the blaze.
Residents of the building say a couch was put in the hallway yesterday by a tenant apparently looking to dispose of it.
Several residents say a homeless man who often walks inside the building and who "smells" has had disputes with tenants who didn't want him to come inside anymore.
The investigator said fire marshals believe the homeless person, whom they describe as "an older man," was the burn victim who was taken to the hospital. He was the only civilian injured in the 3:55 a.m. fire.
They suspect the victim may've been "lit up" by a building resident trying to send a message that he is unwelcome,the investigator said.
Fire marshals were joined this morning by the NYPD arson and explosion squad at the scene of the one-alarm fire that was quickly contained.
No fire code violations are noted on the City's Department of Buildings website. Several evacuated residents complained about a lack of hallway sprinklers and fire alarms, although it's not clear that either is required under City regulations for a structure of this age and size.