LONDON — The family of Milly Dowler, the teenage murder victim whose voice mail messages were illegally intercepted by The News of the World, has been offered a multimillion-dollar settlement by the tabloid’s parent company, a person with knowledge of the negotiations said Monday.

The person said the company, Rupert Murdoch’s News International, had offered about $3.2 million to the Dowler family, with an additional payment of about $1.6 million to go to charity.

The News of the World is believed to have hacked into the voice mails of hundreds, possibly thousands, of people, including celebrities and politicians. Widespread public revulsion resulted from the revelation in July that its victims included the 13-year-old Milly Dowler, who disappeared in 2002 and whose messages were intercepted and erased to make room for new ones even as her family searched for her.

That disclosure ultimately led the Murdochs to close The News of the World, the government to open several inquiries into the matter and the police to expand their criminal investigation into the paper’s conduct.