The U.S. Federal Deposit Insurance Corporation is planning to exempt smaller lenders from kicking in extra money to replenish the government's bedrock deposit insurance fund, and instead saddle the biggest banks with much of the bill, Bloomberg News reported Thursday, citing people familiar with the matter.

The FDIC is planning to release a highly anticipated proposal for refilling its deposit insurance fund as soon as next week, the report added.

The regulator declined to comment when reached out by Reuters.

Smaller lenders with less than $10 billion in assets wouldn't have to pay, Bloomberg News reported, adding that there were more than 4,000 institutions under that threshold at the end of last year.

The FDIC and its flagship deposit insurance fund have been active since the Great Depression to provide an orderly resolution for failed banks and to reimburse certain customer accounts.

The regulator estimates the failure of Silicon Valley Bank will cost the deposit insurance fund $20 billion.