Volkswagen AG is on the hunt for self-driving technology and recently tried to buy Aurora Innovation, an autonomous-driving startup founded by veterans of Tesla Inc. and Alphabet Inc., according to people familiar with the matter. The German carmaker has been scouring Silicon Valley for targets or partnerships that can help it develop self-driving cars and other mobility technology. Volkswagen had talks to buy Aurora, which is already a partner, only to be rebuffed because the Palo Alto, Calif.-based company wanted to maintain its independence and work with multiple carmakers, said the people, who asked not to be named because the discussions are private. For Volkswagen, the search to purchase self-driving technology is a play to catch up to rivals that have forged ahead for several years. Alphabet’s Waymo unit is seen as the leader, and rival automakers have bought self-driving technology developers. Buying Aurora or another company would follow moves by rivals to align with AI specia...