The device, used by an shooter in last year's San Bernardino, California attack, fueled a high-profile legal battle between Apple and the government, which hoped to force Apple to unlock the phone. The FBI eventually breached it with the help of an unidentified third party, and it was unclear whether Apple would find out about the tool used.
The agency wants to tell the White House it "knows so little" about the method that it would not make sense to internally review whether to tell Apple about it, the WSJ said. The paper reported the decision would leave Apple not knowing what security gaps exist in some phones.
The FBI pointed CNBC to comments earlier Tuesday by Director James Comey, who said the agency is "in the midst" of determining whether the vulnerability in Apple's software should be submitted for possible disclosure to the company. He said the FBI needs to determine what it knows about the vulnerability.
"That's something that we've been sorting out the last couple of weeks. I think we're close to a resolution but I'm not ready to make news with it yet," Comey said.
Apple did not immediately respond to CNBC's request for comment.
The case sparked a public exchange of barbs between the tech giant and authorities, re-igniting a debate about the trade-off between privacy and national security. Apple and others in the tech community warned of a possible abuse of power if the government could compel Apple to unlock the phone.
The FBI and some lawmakers, meanwhile, said some concessions are necessary to investigate and prevent attacks.
Comey previously suggested the FBI spent more than $1 million to get into the phone.