Legislation has been proposed in more than a dozen states to require the groups to disclose their donors.
The states are motivated by the lack of progress at the federal level in pushing those groups to disclose their contributors if they engage in campaigns, as candidates and political action committees are required to do, the Times says.
Meanwhile, at the federal level, Sen. Carl Levin, D-Mich., plans to use his post as chairman of the Permanent Subcommittee on Investigations to press for greater oversight of the groups.
The Securities and Exchange Commission is considering a rule to require publicly traded corporations to reveal their political donations.
And Sens. Ron Wyden, D-Ore., and Lisa Murkowski, R-Alaska, last month unveiled a disclosure bill.
Opponents say making donors public would infringe on their privacy and could intimidate some, keeping them from participating in politics.