The Journal cited people familiar with the matter.
A Cerberus spokesman declined to comment to The Associated Press.
The newspaper reported on its Web site Friday that Chief Executive Stephen Feinberg and co-founder William Richter wrote to clients Thursday that they were "surprised" by the response to a plan the company announced last month to reconfigure its funds. The shift gives investors a chance to withdraw their investments.
Cerberus lost 24.5 percent on investments in 2008 and is up about 3 percent this year, the Journal reported. By comparison, the Standard & Poor's 500 index tumbled 38.5 percent last year and is up 13.9 percent in 2009.
The new fund would charge lower fees but require investors to keep their money invested longer. The Journal said management had said it expected to maintain more than half the assets in a new fund.
The newspaper reported that Cerberus' hedge funds have about $7.7 billion in assets in portfolios.