Mark Lewis said the three were a "well-known sports person", a sports person not in the public eye and a US citizen.
"The News of the World had thousands of people they hacked. Some of them were in America at the time, either travelling or resident there," he said.
The now defunct paper's owner, News International, has declined to comment.
Parent company News Corporation - chaired by Rupert Murdoch - shut the News of the World (NoW) after the scale of phone hacking at the tabloid emerged.
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News Corporation also withdrew its bid to buy the remaining 61% stake in satellite broadcaster BSkyB saying it had become "too difficult to progress in this climate".