They include crime victims, celebrities, politicians and sports figures, The Guardian reported Saturday.
"We are confident we have have personally contacted all the people who have been hacked or are likely to have been hacked," Sue Akers, a deputy assistant commissioner at the Metropolitan Police, told The London Times.
"But there is a raft of people still to be spoken to who are potential targets, but are unlikely to have been hacked."
Police had previously identified 5,800 names from the notebooks of Glenn Mulcaire, the private investigator who had worked for the News of the World.
A police spokesman said it would be incorrect to conclude the estimated 5,000 names in Mulcaire's notebooks not identified as hacking victims had not been hacked.