Michael Silverleaf, the lawyer for News Group, which publishes News of The World, said the company last week offered to settle the case with Miller for 100,000 pounds (around $165,000). She has 21 days to accept the settlement. Seven other claimants also received apologies from the newspaper.
Silverleaf argued that Miller's case should not be allowed to continue because she is not likely to win more than the settlement amount.
"She cannot realistically recover more than we are offering," he told the judge.
But Miller's lawyer, Hugh Tomlinson, said money was not the primary motivation for many of the claimants.
"Damages are an aspect, but when private Alexander Wang Shoes information is involved, the kind of relief people are looking for goes beyond simply monetary compensation," he said.
The paper acknowledged last week the practice of illegal hacking was more widespread than it had maintained. For a long time, News of The World insisted that the practice was confined to two rogue employees, who were jailed in 2007 for eavesdropping on voicemail messages of royal employees.