Bruce Berkowitz, a mutual-fund manager with a history of bold bets, is doubling down on a risky wager that the government ultimately will sell mortgage giants Fannie Mae and Freddie Mac back to private investors.

Mr. Berkowitz is reopening his $8 billion Fairholme Fund to new investors to look for new investment opportunities, including potentially increasing his stake in Fannie and Freddie, Mr. Berkowitz said in an interview.

Mr....