MINNEAPOLIS—Federal Reserve Bank of Minneapolis President Neel Kashkari said Monday that he wants to consider bold options for ending “too big to fail” once and for all, at a conference he organized exploring whether the country’s biggest banks should be broken up to prevent future bailouts.

The “Ending Too Big to Fail” symposium, with its own Twitter hashtag “EndingTBTF,” was announced by Mr. Kashkari in February, shortly after he took the reins as president of the Minneapolis Fed in January.

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