Police had earlier said the victim had been identified by Britt's parents as the wide receiver's brother but later said they are not biologically related.
"They tell everyone they are brothers," Jersey City Police Capt. Edgar Martinez told the newspaper. "They are not."
Britt took his friend to Jersey City Medical Center early Sunday morning but did not answer officers' questions about what caused the stabbing, police told The Tennessean.
"We are looking to speak to Mr. Britt in reference to the incident," Martinez told the newspaper. "We are currently in the process of trying to do that."
Britt's friend was treated for a non-life-threatening stab wound to the left side of his back, according to the newspaper.
Before police had clarified that the victim wasn't Britt's brother, the receiver had released a statement saying that the two men are not related.
Britt released a statement through a spokesman late Sunday night that he had driven an injured friend -- not his brother -- to the hospital, but was not involved in the incident, and that he was cooperating with police.
The NFL suspended Britt for Tennessee's season opener against New England after the 24-year-old was arrested July 20 for driving under the influence. It was his eighth incident with police since the Titans drafted him in the first round in 2009. He also visited NFL commissioner Roger Goodell a year ago and received a stern reminder to behave.