An investigation into former Berkshire Hathaway executive David Sokol over stock trading while he was at the company appears to be ongoing, Berkshire Chief Executive Officer Warren Buffett told CNBC on Monday.

Buffett also said Sokol had not been his designated successor. In an investor letter on Saturday, Buffett said Berkshire's board had identified the person who would succeed him as CEO; he said Monday that person had been the same for years now.

(Reporting By Ben Berkowitz)