In a quarterly regulatory disclosure filed this month, the Warren Buffett-owned company terminated credit-default swaps insuring $8.25 billion of municipal debt.
The paper said the early termination is deepening questions among some investors about the risks of buying debt issued by cities, states and other public entities.
The WSJ quoted the source as saying that Buffett's bet that more than a dozen U.S. states would keep paying their bills on time had been made before the financial crisis.
The insurance-like contracts, which required Berkshire to pay in the event of bond defaults, were bought by Lehman Brothers Holdings Inc in 2007, more than a year before the firm filed for bankruptcy, the WSJ quoted the source as saying.
Buffett declined to comment on the details of the termination with the Lehman Brothers estate, the paper added. It is not clear if the move would leave the company with a profit or loss on the wager.
Berkshire was not immediately available for comment outside regular office hours.