Warren Buffett earlier this year offered to invest $3 billion in Uber Technologies Inc., but the two sides couldn’t agree on the terms, according to a person familiar with the matter.

The talks between Mr. Buffett’s Berkshire Hathaway Inc. and Uber, reported earlier by Bloomberg News, came on the heels of a multibillion investment in the ride-hailing firm by SoftBank Group Inc. In January, the Japanese firm invested $1.25 billion directly in Uber at around a $70 billion valuation, and bought another $6.5 billion worth of employees...