Four people have issued High Court claims against the Daily and Sunday Mirror and The People.
The claims allege "breach of confidence and misuse of private information" relating to the "interception and/or misuse of mobile phone voicemail messages and/or the interception of telephone account".
The Financial Times reports that no particulars of the claims have been filed as yet.
The four claimants, represented by media lawyer Mark Lewis, who also represented other celebrities and claimants in action taken against News International, have four months to serve claims on Trinity Mirror, the newspaper said.
More top news
Northern Ireland's Health Minister Jim Wells has quit after sparking controversy over comments about gay marriage.
Prince Harry may not be able to meet his new niece or nephew until mid-May unless the royal baby puts in a speedy appearance.
A British climber trapped on Mount Everest after the earthquake in Nepal has said rescuers face "a race against time" to reach his group