"We have not yet decided whom the case is going to be directed against," lawyer Lars Sandberg told AFP, adding though that the targets are likely to be "four people (already) charged as well as firms linked to the site."
Sandberg has been hired on behalf of the US musicians by British law firm Web Sheriff, which wants to claim "several million dollars" in damages in both Sweden and the United States, he said.
In March Swedish prosecutors charged four people they believed to be behind the site. The music industry has been engaged in a battle for many years to stop people downloading songs on the Internet for free.
In November last year, The Local spoke to Web Sheriff President John Giacobbi, who said that the time had come for The Pirate Bay's founders to pay their dues.
"Because they're based in Sweden they assume that George Lucas and Universal won't come after them - and they have so far been proved right," he said.
According to Giacobbi, The Pirate Bay had previously been able to "hide behind Sweden's lax laws". But these law had gradually become tougher, he said, and could now be used to pin down the BitTorrent giant.
Pirate Bay spokesman Peter Sunde told The Local that Giacobbi had "no clue" what he was doing but that he was welcome to try to sue the file sharing site.