News Corporation chief Rupert Murdoch has pledged to donate £1 million to charity as part of the settlement to the family of Milly Dowler.
The schoolgirl, who was abducted and killed by Levi Bellfield in 2002, is believed to have had her phone hacked by a private investigator working for the News of the World after she was reported missing.
In a separate payout, the Dowler family is expected to receive upwards of £2 million from News International, the publisher of the newspaper.
On Monday, News International said it was in “advance negotiations” with the family about a compensation package that would reflect the “exceptional circumstances” of the case.
The package for the Dowler family is expected to include a further donation to a charity of the family’s choice.
A News International spokesman said: "No final agreement has yet been reached, but we hope to conclude the discussions as quickly as possible."
The revelation that the missing schoolgirl’s voicemails were intercepted led to a public outcry, which eventually resulted in the closure of the newspaper in July.
Murdoch has since apologised to the Dowlers in person.
Mark Lewis, the lawyer for the Dowler family, commented that Murdoch had been "humbled" by the meeting.
The family has since been named as "core participants" in the Leveson inquiry into media conduct.
Labour MP Tom Watson, who has long campaigned on the issue of phone hacking, said that if true he hoped the settlement would give the family "some peace and some privacy".
"They've had a terrible year and this will hopefully be a settlement for them," he told the BBC.
But Watson said Rupert Murdoch could face a backlash from News International shareholders as they had been assured the total payments to victims of hacking would not exceed £20m.
"With a two million settlement for a single case when there were other victims of crime...that sum is going to be dramatically more than that," he said.
The News of the World has previously reached settlements with actress Sienna Miller, who was paid £100,000 after her voicemail was intercepted, and football pundit Andy Gray, who accepted £20,000.
The Metropolitan Police are still contacting victims of the phone hacking scandal following the seizure of notebooks from Glenn Mulcaire, a private investigator who worked for the News of the World.