Milly Dowler's family are close to reaching a settlement deal with News of the World, News International have confirmed.
In July reports emerged that the now-defunct newspaper had hacked into the murdered teenager's phone.
Her family have been named as "core participants" in the Leveson inquiry into media conduct.
According to the Guardian, News International have offered the family £2m.
And Sky News has reported that Rupert Murdoch will also donate a further £1m to charity.
A News International spokesman told the Press Association: "News International confirms it is in advanced negotiations with the Dowler family regarding their compensation settlement.
"No final agreement has yet been reached, but we hope to conclude the discussions as quickly as possible."
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 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.
shareholders will be very concerned to hear this this evening