The Federal Deposit Insurance Corp., facing almost $23 billion in costs from recent bank failures, is considering steering a larger-than-usual portion of that burden to the nation’s biggest banks, according to people with knowledge of the matter.

The agency has said it plans to propose a so-called special assessment on the industry in May to shore up a $128 billion deposit insurance fund that’s set to take hits after the recent collapses of Silicon Valley Bank and Signature Bank. The regulator — under political pressure to spare small banks — has noted it has latitude in how it sets those fees.