The final total of people whose phones were hacked by the News of the World will be about 800, it has been reported.
The head of Scotland Yard's hacking inquiry, Operation Weeting, told The Times that she was confident her officers had met all the likely victims of the tabloid's activities.
Deputy Assistant Commissioner Sue Akers told the newspaper: "We are confident we have personally contacted all the people who have been hacked or are likely to have been hacked."
She added: "There is a raft of people still to be spoken to who are potential targets, but are unlikely to have been hacked."
A further 1,200 people have been in contact with the inquiry, but they are not believed to have been hacked or are not named in the notebooks seized from the private detective Glenn Mulcaire, who was employed by the News of the World, the newspaper said.
Thousands more people will be contacted, but it is thought that because of the lack of personal information about them, they are unlikely to have been hacked, it added.
A Scotland Yard spokesman said: "Operation Weeting has been in contact with or been contacted by 2,037 people, of which in the region of 803 are 'victims', whose names have appeared in the material."
The scandal led to the closure of the News of the World after 168 years, prompted a major public inquiry, and forced the resignation of Metropolitan Police commissioner Sir Paul Stephenson and assistant commissioner John Yates.
It was known that some 1,800 people had come forward to express fears that they may have been hacked.